Basically, all betta that you buy in the pet store are exactly the same species, known as Betta Spendens. There are however, many different variations of the species due to domestic breeders. This is where we get into different tail types and colors, but regardless of color/tailtype, since they are the same species they require the same params and care.
There ARE different species of betta, and this is where things get a little more exotic, and since I haven't the slightest clue about wild betta, Ill let someone well versed in the subject explains their differences from betta splendens. However, I can provide you with this helpful link, which has a list of the different species and links to pages with info about them.