Yes.. it goes like this:
lifting legs to body-lower rectus abdominis or lower abs examples: reverse crunches, hanging knee or hanging leg raises
lifting torso- upper rectus abdominis or upper abs examples: crunches, hanging from feet from bar, cable crunches
The same also applies to obliques:
lifting legs to the side: obliques but stresses lower portion a bit more
lifting torso to the side: obliques but stresses upper portion a bit more.
The above is not a strict handbook.. some exercises such as hanging knee raises will also work transverse abdominis. A swiss ball jack knife will work your entire core including your lower back but with an emphasis on lower abs
To answer your last question, lifting knees to chest rather than lifting legs and feet(hanging knee versus hanging leg raises) is just a range of difficulty. They both work the same muscles.. lifting legs as a whole is just more difficult. once you've mastered hanging knee raises you can do hanging leg raises.. the angle just makes your bottom half heavier. Just be sure you are using your core and not your legs to do the lift.. many people use their legs and hip flexors to bring their legs up in a hanging leg raise. This takes away from your core. After mastering hanging leg raises, you can do hanging pike-ups where you bring your legs past 90 degrees until your toes touch the grip bar.