I have been thinking for some time about exactly how can these 3 games be relevant to each other. Nomura stated they won't share continuation on the story part, but the thing is, we have the same mythology (goddess Etro and stuff), we have our l'Cie and so on.
So, i think the games might not be directly relevant to one another, but they surely seem to share the same universe. Plus, when i finished XIII i made a crazy thought of "alright, XIII takes place on Cocoon now, while type-0 takes place in Pulse fuuurther in to the past, and Versus XIII further to the future!" So, i think they actually take place in the same world, only with huge chronological distance. What do you think about it?
I can't put out of my mind that Ivalice Alliance had such a connection, so there must be a reason these games belong in the same compilation besides "having to do with crystals", which is a reccuring theme in the series anyway.
"Divine Etro. Go peacefully to your rest. I will stand guard over your legacy."