That really depends on the paper itself. Usually, sketch paper will be too thin for watercolors to come out in a satisfactory manner. That being said, it all depends on what your final outcome is. Where the piece will be displayed, and what effects you are trying to get.
Watercolor paper is, normally, quite a bit heavier and made from cotton. Basic watercolor paper, 140lb, is okay for practice and will tend to buckle unless stretched. The expensive 300lb paper is where professionals tend to land. In any case, the paint pools and absorbs differently than normal paper, and gives you options around blending, washes, etc. that you can't otherwise get.
Traditional paper, made from wood fibers, is much thinner and absorbs the pigment faster, will generally buckle and warp rapidly and is much more likely to rip and tear when wet. It's just not designed for that.
In any event, sheet watercolor paper can be had and you can always cut it into smaller sizes for practice, which is pretty common anyways. The cheaper option will only frustrate and disappoint, it's already a challenging medium, don't make it hard on yourself.
Depends: are you sketching (with pencils, presumably), or are you painting with watercolors? :)
If you're sketching/drawing with pencils and other dry media, the sketching paper is probably to be preferred, because the vast majority of what is available as "watercolor paper" is cold-press, i.e. pebbly/rough surfaced.
If you're painting with watercolors, unless you're using a particularly dry technique, the sketch paper will probably simply fall apart on you. You need to use a paper that is designed to withstand watercolor techniques such as washes and blending, which pretty much means using the heaviest-weight watercolor paper you can afford, or using a lighter weight and investing in the equipment to stretch it as it dries. Either way, though, a paper that tears when wet will not cut it.
And if you're doing neither sketching nor watercolors, but, say, pen and ink drawings, neither sketch paper nor watercolor paper will be particularly satisfactory. Moral of the story: match the paper to the material/technique.
If you want the best results in your paintings, you also need to find the best watercolor paper brand. This way, you will not only have a perfect texture but also incredible results.
There are various factors that you need to keep in mind when you try to find the best one. The material, quality, texture, roughness of the watercolor paper matters a lot. Moreover, if you plan on selling your paintings, the finished painting has to be impressive.