Viscera, you are actually correct about this. The first game was indeed about an ex Navy SEAL who gets dragged into a bad situation. There was indeed some nutty psycho doctor who makes the mutant apes and they basically go ape S*** on everyone. So part 2 really diverts from the original story. Actually 2 and 1 have NOTHING in common.
Hope this helps.
Actually they do have ONE thing in common. Well, two.
Those are:
1. Far
2. Cry
That's it.