There are alusions to most of the final fantasy series in FF14 ranging from FF1 all the way to FF12. Lightning from FF13 even had her own event. So while they are all diffrent worlds, remember that they all have a loose connection via the void. That seems to be the one and only comman factor and possibly what ultimatly seperates all the final fantasy games' worlds from each other.

So are they the same world? No, the Devs have said Eorzia is in it's own world unrelated from FF11, FF12, ect. Are Ivaliace and Eorzia connected? Only by the void its self which seperates all the worlds of final fantasy.