I like how "FF Versus XIII" says it's an entirely different world with entirely different characters than "FF XIII"... okayyy... wouldn't that just make it seperate from XIII altogether, then?
It'd be like calling FF IX (with Zidane, etc.) "Final Fantasy Versus VIII."
I think there was some tiny note about multiplayer on one page I read, but it seemed associated with the mobile phone version. I think the other 2 games will be single player.
I also had the impression that "Versus" was in the same world/universe, just with different people and on a related but different storyline. The two games are supposed to play differently (one more action-oriented), but are still related to one overarching story. Or at least that's how I read it.
I was really excited by the trailer video, and will be eagerly awaiting this one (as opposed to my general but not extremely-high interest in FFXII).
Edit: Oops, just reread and saw "different worlds" in there. Well, at least "common mythos" makes it sound like they're still related to each other by a lot more than their name.