You pretty well answered your own question. All those you mentioned are just different variations of the sport of MountainBiking.... Each is pretty well self explanatory by their name, with the exception of "Freeride", which is usually riding across/up/down whatever happens to be available. XC (cross country) is probably the most popular type, at least with those people not in the larger cities.

You might want to search the Forums, as this question has been asked several times before....