If I am correct, FF XIII, FF XIII Versus, and FF XIII Agito are all based on the same world setting. All Final Fantasy games have been completely unrelated to each other when a core game is released with a new number. They seem to use the number to designate that games are related, occuring in the same world setting.
Thats why Final Fantasy X-2 was X-2 as opposed to Final Fantasy XI. The game was a direct sequel, as opposed to another completely different story.
Tag: Hawk - Reluctant Dark Messiah (provided by fkusumot)