Buddhism teaches Anatta (not self) and the Nibbana is the final goal. You can't find them in Advaita Vedanta. Buddism also has Noble Eightfold Path with a clear set of instructions as to how to attain Nibbana. In my opinion, it is just more than semantics. The only way to be sure is to study and practice both.
In merely the first 10 seconds, the video refers to alien ideas, such as "immortality" & "Self".
The video then talks about finding happiness & ending suffering, which is the aim of many philosophies; including hedonism. Even monkeys seek to avoid suffering & find pleasure.
The video then says "if you knew yourself as you truly are all your suffering would be overcome". It says "the real Self is the witness consciousness- the one unchanging experiencer - the real me"... "The witness consciousness is freedom from the person & what is witnessed". These ideas are alien to Buddhism, particularly the permanence of consciousness and the idea of a "real me".
Also, the speaker never stops referring to a "you", as though there is a "you".
The video then says "when you [lol] stop there saying all things I am not, you [lol] have Buddhism and fall short of Vedanta". This is wrong. Buddhism does not have the doctrine of "I AM NOT". The doctrine of Buddhism is "this is not a me; this is not a mine; this is not a self".
Then the video wrongly said Hindu Atman & Buddhist Anatta are the same thing from a non-dualistic perspective. In actuality, original Buddhism does not teach self (atta; atthattā) & not-self (anatta) are a "duality". Original Buddhism teaches "I am" ("atthattā") and "I am not" ("natthattā") are dualities because both ideas still believe in an "I", i.e. an "I" that is and an "I" that is not. "Not-self" ("anatta") is not part of any duality that is transcended into non-duality. "Not-self" ("anatta") is the inherent characteristic of everything, without exception. Both the "dual" & "non-dual" are "anatta".
Then the video falsely says Buddhism does not believe there are "things". This is wrong and confused. The original Buddhism of the Buddha says there are "things" ("dhammas"). It is the Mahayana Buddhism of the philosopher Nagarjuna that purports there are no things. The speaker actually quotes Nagarjuna, which shows the speaker falsely believes Nagarjuna is the Buddha.
In conclusion, there is nothing I heard in the video that is related to Buddhism. The goal of Buddhism is to perfect something called DISPASSION and END CRAVING. The speaker in the video appears devoted to, delighting in & even worshiping the delusion of a silent unchanging witness. This is not Buddhism. Buddhism does not delight in anything. Buddhism says delight is the root of suffering. Buddhism says any type of consciousness, gross or subtle, is dukkham (unsatisfactory; not warranting delight).
Sutta show that language and the verbalization of thought are by default with delusion not without delusion.
We say 'an apple', maybe we can point to one like we can point out ourselves in a photograph or otherwise point at our body.
If we analyze the semantics of the word 'apple' we see that it's referent is included in either;
shapes & colors made visible by the eye; or tastes, sounds, smells and tactile sensations of which we think as included in class "apple"
the idea or the class itself of which we can only think, it's invisible to the eye, seen by intellect as ideation.
The idea of an apple is mind-made, one can only think of what the senses present as an apple.
Furthermore we know it's more like a folder on a desktop than a file because when we point at an apple we can be said to be seen pointing at what is rightly described as to carbon molecules or the electro-magnetic process with no apple-element therein.
Like an apple the ideas of self as personal pronouns is great and useful way to communicate as words have proven to be. We just ask for an apple, no need to explain what we need in terms of mathematics and special relativity but mathematics and special relativity systems predict outcomes which are hard to see & grasp.
When going by our name. We know our name is just our name and isn't really a part of the body or mind.
The self is just like that as well, useful in some sense but not really a thing.
If we want to know how senses & intellect work, to predict outcomes by developing understanding, we then have no use for the idea of self because it is never rightly inferred as an apple is never an element of a molecular structure of a fruit, so a self is not among elements which the senses present or what can be known otherwise, it is included as a class of ideas [classed as to object of ideation]. The ideas of apple & self are based on default understanding of what the senses present, this is by default very primitive kind of understanding which is with delusion.
One thinks then in terms of elements known to be true with due inference and one sees that there is no self among them, nor is there a self apart nor are they together taken to be a self.
There are doctrines of self like there is the doctrine of whatnot, doesn't mean it's true.
It's important to grasp that world is delusional, is not without delusion. Therefore delusional ideas are it's basis and are an integral principle of it's description.
Basically if want to be stuck in delusion obv keep wrong ideas and not understanding. If want to end delusion one should develop knowledge and know faulty ideas as faulty ideas.
In the video, the speaker said:
Vedanta is about Atma (the Self). ... the next word is Sakshi (Witness) ... What is the Self? Is it this bundle of flesh and blood? Is this person in the body? The mind, the intellect, the memory, the likes and dislikes, the knowledge, the person I think I am - is that the Self? Or is it something beyond that? According to Vedanta, you are the real Self, is the Witness-Consciousness. It is that which experiences. It is that which experiences in the waking state, in the dream state, in the deep sleep state. The one unchanging experiencer, which enables all experience. What does that mean?
Take a simple methodology. It's a philosophical enquiry into who am I? ... This technique is called the seer and the seen. ... Remember, the purpose is to discover the Atma, the real Self. It's about discovering who you really are. ... It says: You are that which experiences. That which is experienced, is not you (the Atma). ...
The speaker goes on to explain how the body, sensory organs, feelings, thoughts, and mind is that which is experienced, so it is not the Self. He says the Self is the Witness-Consciousness. He says you are not the person (which is the ego-identity or ego-personality constructed by the mind) - you are that which is aware of the person. He calls it the illuminer of the body-mind. He calls the Atma unchanging, while all the changing things are that which is experienced, not the experiencer.
Somewhere further in the video, he says Buddhist Madhyamaka has emptiness but even that emptiness must be experienced by a Witness-Consciousness.
Then further on, he goes on to explain what Advaita teaches, which is that all the changing things are not separate from Brahman, but rather manifested from Brahman and experienced by it. He provides the example that one witnesses the contents of one's dream, but the dream is also part of the mind and not separate from it. Then he says that God is the experiencer through all beings.
OP: Are the differences between Advaita Vedanta and Buddhism merely semantic/perspective? ... having studied Buddhism and Advaita Vedanta, I've seen that the differences between the two are almost non-existent.
The answer depends on what you define as Buddhism.
If you look at Mahayana Buddhism, I would say different Mahayana schools have different opinions.
From the following statement from this page, we see an explanation of Yogacara philosophy that sounds similar to Advaita Vedanta, yet is not exactly the same. This answer shows how Yogacara is different from Advaita.
The central thesis in the Yogācāra philosophy, the theory of the two truths echoes is the assertion that all that is conventionally real is only ideas, representations, images, creations of the mind, and that there is no conventionally real object that exists outside the mind to which it corresponds. These ideas are only objects of any cognition. The whole universe is a mental universe. All physical objects are only fiction, they are unreal even by the conventional standard, similar to a dream, a mirage, a magical illusion, where what we perceive are only products of our mind, without a real external existence.
All these arguments based on the facts of experience show that objects do not exist really outside the mind, that they are products of mental creation and that their appearance is entirely mind dependent. Therefore the Yogācāra's theory of the two truths concludes that the whole world is a product of mind—it is the collective mental actions (karma) of all beings. All living beings see the same world because of the identical maturation of their karmic consequences. Since the karmic histories of beings are same, there is homogeneity in the way in which the world is experienced and perceived. This is the reason there is an orderly world instead of chaotic and arbitrariness. This is also the reason behind the impressions of the objectivity of the world.
... The idealism of Yogācāra holds nondual mind as the only ultimate reality and the external world as merely conventional truths.
The same page explains Nagarjuna's Madhyamaka (below). Based on the following, it is clear that Advaita Vedanta is incompatible with Madhyamaka, because Madhyamaka advocates groundlessness i.e. everything is empty of intrinsic essense, including consciousness and emptiness itself. On the other hand, in Advaita Vedanta, Brahman is the substratum or ground for everything (see Vivekachudamani 225-231, 289).
There is absolutely nothing that has intrinsic essence in Madhyamaka, not even consciousness, not even emptiness. Empty of intrinsic essence does not mean unreality or non-existence, but is rather because everything is conditioned, changing and dependently originated.
On Nāgārjuna's Madhyamaka all things including ultimate truth are ultimately unreal, empty (śūnya) of any intrinsic nature (svabhāva) including the emptiness (śūnyatā) itself, therefore all are groundless. In this sense a Mādhyamika (a proponent of the Madhyamaka thought) is a an advocate of the emptiness (śūnyavādin), advocate of the intrinsic unreality (niḥsvabhāvavādin), groundlessness, essencelessness, or carelessness. Nevertheless to assert that all things are empty of any intrinsic reality, for Nāgārjuna, is not to undermine the existential status of things as simply nothing. On the contrary, Nāgārjuna argues, to assert that the things are empty of any intrinsic reality is to explain the way things really are as causally conditioned phenomena (pratītyasamputpaṅhā)
Nāgārjuna's central argument to support his radical non-foundationalist theory of the two truths draws upon an understanding of conventional truth as tied to dependently arisen phenomena, and ultimate truth as tied to emptiness of the intrinsic nature. Since the former and the latter are coconstitutive of each other, in that each entials the other, ultimate reality is tied to being that which is conventionally real. Nāgārjuna advances important arguments justifying the correlation between conventional truth vis-à-vis dependent arising, and emptiness vis-à-vis ultimate truth. These arguments bring home their epistemological and ontological correlations ([MMK] 24.14; Dbu ma tsa 15a). He argues that wherever applies emptiness as the ultimate reality, there applies the causal efficacy of conventional reality and wherever emptiness does not apply as the ultimate reality, there does not apply the causal efficacy of conventional reality (Vig.71) (Dbu ma tsa 29a). According to Nāgārjuna, ultimate reality's being empty of any intrinsic reality affords conventional reality its causal efficacy since being ultimately empty is identical to being causally produced, conventionally. This must be so since, for Nāgārjuna, “there is no thing that is not dependently arisen; therefore, there is no such thing that is not empty” ([MMK] 24.19, Dbu ma tsa 15a).
From this page (quoted below), Candrakirti (a Madhyamika) criticizes Yogacara:
One further Buddhist movement that Candrakīrti criticizes is the Yogācāra school, which he presents as advocating a form of subjective idealism. Their claim that the world of experience is consciousness only and that the contents of consciousness cannot be objects external to consciousness itself is supported by several texts within the Mahāyāna scriptural tradition. Candrakīrti explains these scriptures as examples of teachings that the Buddha gave to counter a particular kind of commonly held wrong view. There are, says Candrakīrti, those who mistakenly believe that all their suffering is due to causes outside themselves; they see themselves as unfortunate victims of a hostile world. The Buddha, wishing to make it clear that the predominant factor in dissatisfaction is the way one thinks about one’s experiences, said, in effect “It’s all in the mind.” It would be a mistake to take that statement literally and to conclude that nothing but consciousness exists and that the world of experience that feels as though it is external to consciousness is in fact produced by consciousness or is inseparable from consciousness. The Yogācāra offers good reasons to show that the contents of consciousness are conditioned and therefore are empty of inherent existence, but they fail to appreciate that exactly the same can be said of awareness itself. In other words, says Candrakīrti, the Yogācāra philosophers fail to acknowledge that everything, including consciousness itself, is empty.
Also the same page (quoted below), mentions Santideva's (a Madhyamika) criticism of Yogacara:
Although beautifully written, Bodhicaryāvatāra does not display much philosophical originality. Its principal contribution is in offering a concise recapitulation of the currents of Madhyamaka thought and of Madhyamaka arguments against Yogācāra monism, which portrays consciousness as the ultimate source of all realities.
But what did the Buddha himself teach? From his own words in the Pali Canon (MN 38):
"Just as fire is classified simply by whatever requisite condition in dependence on which it burns — a fire that burns in dependence on wood is classified simply as a wood-fire, a fire that burns in dependence on wood-chips is classified simply as a wood-chip-fire; a fire that burns in dependence on grass is classified simply as a grass-fire; a fire that burns in dependence on cow-dung is classified simply as a cow-dung-fire; a fire that burns in dependence on chaff is classified simply as a chaff-fire; a fire that burns in dependence on rubbish is classified simply as a rubbish-fire — in the same way, consciousness is classified simply by the requisite condition in dependence on which it arises. Consciousness that arises in dependence on the eye & forms is classified simply as eye-consciousness. Consciousness that arises in dependence on the ear & sounds is classified simply as ear-consciousness. Consciousness that arises in dependence on the nose & aromas is classified simply as nose-consciousness. Consciousness that arises in dependence on the tongue & flavors is classified simply as tongue-consciousness. Consciousness that arises in dependence on the body & tactile sensations is classified simply as body-consciousness. Consciousness that arises in dependence on the intellect & ideas is classified simply as intellect-consciousness.
The Buddha rubbished any notion of a permanent independent universal consciousness and explained how consciousness is linked to the six senses (including intellect).
From the same sutta:
The Blessed One then asked him: “Sāti, is it true that the following pernicious view has arisen in you: ‘As I understand the Dhamma taught by the Blessed One, it is this same consciousness that runs and wanders through the round of rebirths, not another’?”
“Exactly so, venerable sir. As I understand the Dhamma taught by the Blessed One, it is this same consciousness that runs and wanders through the round of rebirths, not another.”
“What is that consciousness, Sāti?”
“Venerable sir, it is that which speaks and feels and experiences here and there the result of good and bad actions.”
“Misguided man, to whom have you ever known me to teach the Dhamma in that way? Misguided man, have I not stated in many ways consciousness to be dependently arisen, since without a condition there is no origination of consciousness? But you, misguided man, have misrepresented us by your wrong grasp and injured yourself and stored up much demerit; for this will lead to your harm and suffering for a long time.”
Here, the Buddha says there is no such thing as permanent consciousness that experiences everything. Rather, it is dependently originated. Please also see this question.