I think it's obvious that all of the FFs are connected. They all have characters named Cid. Many of them have magic, chocobos, and moogles.

Also, all of them have trees, mountains, and oceans. They have humanlike characters as well. This is obviously designed to show the series is all connected.

Furthermore, imps/goblins exist in other RPGs as well, and other RPGs have magic like "cure" and "fire." This shows that not only do all FFs take place in the same world, but all RPGs, in fact, take place in the same world.

My red pen and "final fantasy" have been mentioned in the same sentence, just now. My red pen and "final fantasy" are all a part of the same world. My world exists within final fantasy, not the other way around. that's how science works!