Spoilers for the lvl 59 Moogle quest and the lvl 60 BRD story quest in the second paragraph:

The story as it is pieced together is that long ago the Moogles all lived on a land in the sky. Then one day a disaster happened. The Moggles speak of fire raining from the sky. This is very likely a calamity. The disaster shattered the land upon which they lived into countless small sky islands. The Moogles who survived the disaster found their lands destroyed and greatly reduced. Struggling with lack of space the Chieftain of the time Moggle Mog called for volunteers to seek out new land for Moggle kind. These Moggles descended from the sky with kupo nuts and never returned.

Its worth noting that a 3rd group of Moggles also survived. In the Sea of Clouds you can find Moggle structures. During the BRD Job quest you discover that the Moggles of these lands once befriended a Siren but the Siren turned on them and slaughtered them with her cursed songs. The survivors sealed her in a wardstone but clearly didn't remain. My guess is they moved to settle in Moghome.