The Nemesis was designed and programmed to eliminate S.T.A.R.S. members which means it would have been following Jill around like mad. The first half of RE3 is set before RE2 which means Leon or Claire wouldn't have been in Raccoon City to see the monster. When Claire and Leon reach Raccoon City and both make it to the Police Station my guess is Nemesis is already at the Clock Tower. Both games have different routes and Raccoon City is huge, meaning it is very easy to miss each another. Thats me theory anyways. As for different enemy's, thats just Capcom introducing newer enemy's to the series a guess, plus the fact the game takes different routes may be a factor.
Hope I helped and if my theory is wrong then please someone clear it up for me!