Oh man Killzone could be hard to explain since I didn't actually beat the first one. All you have to know is that Multiplayer is the most amazing thing since sliced bread. I never had so much fun with a multiplayer game before, Gears and Halo had decent multiplayer but it didn't last me very long. The ranking, perks, and various maps are just too awesome haha I didn't experience any lag on there like I do with XBL and the community is 5000 times better, mostly because people don't talk but you sure as hell don't have millions of 12 year olds on there. It's not similar to Gears of War 2 in the least bit, it's an FPS and an amazing one at that, check out my video of the game and you can get an idea of what it is like.
http://www.youtube.com/watch?v=k4Bfd5s-Gik
As far as the difference between FF13 and FFvs13 there's a few things
FF13 is a turn based RPG where as FFvs13 is an Action RPG much to the likes of Kingdom Hearts, which isn't surprising since Tetsuya Nomura is directing the game. FFvs13 is a MUCH darker game it seems, looks very unique compared to other Final Fantasy games. They are both set in the same "universe" but are not completely related story wise.
This should better explain things
'Within recent Japanese gaming magazine interviews, Tetsuya Nomura has stated that Versus XIII's gameplay will be a realistic derivation of Kingdom Hearts battle system with some elements of a third-person shooter - similar to Square Enix's Dirge of Cerberus. Nomura has also stated that the game will depart from the light and magical aesthetic of his previous directorial games (i.e. Kingdom Hearts) and opt for a darker, bleaker world that is intended to counter previous Final Fantasy installments. In formulating a realistic world, Nomura has stated that he wants the characters to be "believable" and thus realistic. As a testament towards his desire for realism; in the PlayStation Premier trailer, in contrast to previous Final Fantasy titles, Versus XIII had a greater display of graphic violence with an instance of blood.
Nomura has also stated in Dengeki PlayStation that he aims to create previously unseen "tricky" battle sequences, reminiscent of the CGI film, Final Fantasy VII Advent Children."