From what I remember reading, Empty Fist is essentially correct. Chen style is the earliest development and bears some resemblance to hard, external arts because it uses more fast, explosive movements. Yang style was next, coming out of Chen, and it puts more ephasis on softness and being relaxed; it's done at a slow, steady pace and doesn't have the explosive movements of Chen style. As for others, I think they're developments out of one or both of these. Wu can be one of two styles though -- there's a Wu that's also called Hao and one that's just called Wu. One book I have indicates that the Wu (W'u) or Hao style came from a combination of Chen and Yang and the Sun style developed out of this. The other Wu style derived just from Yang and the same book calls it Small Frame Yang Style. I'm not well versed in the differences, but I have enough books that if I felt like doing it, I could probaby go through them and come up with something better than this. But I need to go to bed soon.
I think dmax999 is right about the "tai chi" or "tai chi chuan" difference in naming. But like Scout_379 said, visit schools and talk to people there. They should be happy to answer your questions. If you want a school that will teach the martial aspects of the art, make sure you ask about that and choose a school that will cover it. Good luck with the search, hopefully what we've said here is of some use to you.