As far as I know, pull-ups and chin-ups are the same thing... Perhaps you are referring to which direction your hands are facing??
Anyways, the major muscle involved with pull-ups is the latisimus dorsi (upper back or lats). You also work the serratus anterior (just outside your pecs), biceps, and forearms. I suppose facing your hands towards you would include the brachialis and work your bicep harder than facing away.
Two fingered pull-ups will also strengthen some muscles in your forearm. Note: there are NO muscles in your fingers and hands, only tendons. Extreme care should be taken when doing these two-fingered jonts, because your muscle will increase in strength significantly faster than the tendons for your fingers. If you aren't careful, you will pull a tendon and be done with this stuff for a LONG time.
As far as push-ups, the pectoralis major (chest or pecs) is the major muscle worked. Also included are: triceps, front deltoids (shoulder muscles), and again the serratus.
Keep up the good work!
I hope this helped,
Rip