They do have a slight one. Both have origins as being part of the XIII series of Fabula Nova Crystalis, which means that they pull from the same mythology for the backdrops. You watch the most recent trailer for Type-0 you'll hear l'Cie brought up and XV may still have some mythology ties to XIII's mythology as well. I don't know if in the rebranding they completely cut all ties with the mythology that was originally going to make up Versus XIII.

But that is about the only tie. Remember even when the games were Agito XIII and Versus XIII they were never going to be in the same world or universe as XIII. The creators just made a mythology that they planned to be used for all three teams, which would then use and interpret the mythology in unique ways to suit the games that they were making. So if you have reservations because of the XIII stigma, you don't have to worry, they aren't connected. No more connected than FFVII and FFVIII are connected because they're in the same franchise sort of connection.