We can't say definitively that they are on separate worlds or not since Square Enix has remained a little vague about the details on the other games in the series. Considering that FFXIII is out though more details on the other games or next in line should help to make those answer clear.
Currently, all we have to go on is that they will share the same mythology, which knowing FF's past games does not have to expressly mean same world. Even if it is the same world, it is pretty clear that they all will have no tying story or character link to each other. They will be distinct and different as well as stand alone that you won't be required to have play the others to understand what you want to play.
That's about all we've heard, which is very old information. So it may have changed since then.
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