Fallout 1 and Fallout 2 aren't directly related either.
Pffffft. You have a picture of The Master from Fallout, you should know then that Fallout and Fallout 2 are inexplicably bound to each other.
1. The Vault Dweller is the ancestor of The Chosen One.
2. Canonized events in Fallout shaped the future of Fallout 2's world.
3. Various factions are tied up to events from TVD's travels.
I know I've skipped on some other points I'm sure someone else will mention.
Anyway, as I see it, F and F2 share the same storyline, but Fallouts with numbers are about the USA as a whole. So IMO, it makes sense 3 portrays another part of the USA aside from California.