Well, that was less of a version and more of a update, even though it was it's own board, it didn't really do anything major, since it was still called "Street Fighter 2" (it took capcom forever to count to 3), So if you call that a sequel, then we should call "Hyper" and "CE" sequels, but their not. Just different versions of the old hat.
(I didn't count the non-made-by-capcom-hacks like rainbow 1 and 2, accelorater, Red Wave, etc.)
SF3 was a complete changing. And is one of the best current fighters, and is arcade perfect (just no coin slots!) on the PS2.
It's more of a "thinking mans" fighter(due to parrys, different supers,). People on the Shoryuken boards call the diehards that play this game "theoryfighter".
And yes, the alpha/zero series are correctly called the prequels to SF2, But after SF1. If you want to get storyline canon picky, the first alpha game never happened canon wise, and starts at Alpha/Zero 2.
Theres a storyline at gamefaqs if it interests you.
(god, i play way to many 2-D fighters.)