The Void is the only thing that ties all these worlds together, which is the absence of The Crystal (or The True Crystal). Without the blessing of the Crystal's light, the world is a terrifying hellish place filled with demons worse even than the Seven Hells.

Now Gilgamesh is a good example with Enkidu, but let's review this: Gilgamesh could easily have the same number of arms in each game but only reveal the others if he chooses to. It's also possible that the Void's power transforms and deforms him like all of the demons that exist in the Void. Enkidu was brought up, but how many times has Enkidu really appeared in the Final Fantasy games? Not that many, and as Torquil said, Gilgamesh states very specifically that he lost his friend Enkidu and named the chicken after him. In most of the games he's searching for his long lost companion.