Long ago, there was what I call the "original cosmos". The wills of Light and Darkness dwelled as one in the aetherial sea within this one dimension. When Hydaelyn expelled Zodiark from the sea and sealed Him within and/or as the moon, the fabric of reality was so stressed that it cracked, and like a broken mirror cast thirteen reflections of the original cosmos, creating one with a total of fourteen worlds (or dimensions). (Source: The Word of the Mother)
That original, primordial dimension from which all of the others sprung is now called the Source; that's where we live (and where Lahabrea and Elidibus are from). At the moment of division, the other worlds were exact copies of the Source aside from varying shards of Light and Darkness, giving each a unique balance. Since that time, each world has been playing out on its own, and has been doing so for so long that the worlds are similar to ours at the core, but aren't much alike superficially. (Source: Koji Fox, Vegas Panel)
Imagine if you could go back 20,000 years and slightly change some things. Send a group of nomads in a different direction, save a few that would have died, kill a few that would have lived. Imagine how different Earth might be today if different settlements had succeeded or failed, if different people started family trees, if certain family trees never came to be, if battles and wars had gone the other way.
Those are the other thirteen worlds (seven of which have been destroyed, another is the void, and another is currently recovering from (almost) a Flood of Light. There's a chance that they might have the same landmasses, but as for whether they'd have the same boundaries and names and religions, the probability is very low. Even just the Calamities we've suffered have shaped the landscape to some degree and our history careened as a result.
SIDENOTE
SE could probably get away with basing an entire expansion on another world when the funding starts running low. Just copy the zones LANDFORM wise (a la Wings of the Goddess) and fill them out completely different in terms of national limits and population traits and such. If we take the Ascians out and finish the main scenario, life on the remaining worlds would be rather stable. The cosmos would still "beautifully broken" (the Ascians want to "heal" it by resurrecting Zodiark and likely destroying just ... just everything), but otherwise stable if the crystals stay out of it. We could go there and face some other great threat. (Hopefully one that doesn't start to make what came before it seem different in context; XI had some issues with that - kinda muddied the perceptions a bit). But I digress.
The Warriors of Darkness look like us mostly because Square Enix though it would be fun to base them off of the CG trailer party, which was just as confusing as it was cool. Their world has life like ours, but not quite the same. Jobs like ours, but not quite the same, and so on. Some of their traits (and probably their names) were probably taken from our world when they got here (potentially they were possessing people or corpses that were here; that part I'm not clear on). Their job titles were the big hint that they were from a place that was similar but not quite.