Right, there are different things going on here.
There are two "spinoffs" for FFX which let you play I think Rikku and Tidus if I remember properly. They're not sequels, they're side stories. They never carry characters over from one game to the next.
In addition, they're coming out with FFXI with is an on line multiplayer game. All of the consoles - including the PS2, XBox, and GameCube - are becoming internet enabled. So this means you'd be able to play on the internet with other people. The XBox is only going to allow broadband, but the PS2 and GameCube will allow phone lines if that's all that you have. It's not ANY different than how you connect to the internet now.
I'll put up some articles on both to make it clearer <img src="/images/graemlins/smile.gif" alt="" />