February 2020 Version Update

You have the real gods, the "celestial avatars", they are embodiments of the elements.
Then you have false gods, the "terrestrial avatars", they're only special because for whatever chance of a reason they escaped the "flattening" of the universe when the original crystal broke apart into the mothercrystals, creating Vana'diel.

If you're familiar with Platonic cosmology, then you'll immediately recognize that the terrestrial avatars are the Ideal Forms of the mundane beasties that we kill by the millions.
In the reforged world, everything would be like them. All dragons would be Bahamuts, all wolves would be Fenrirs, all birds would be Phoenixes, etc.

Siren is just the ideal Harpeia. She also is that devilbell from the geomancer quests, and the ultimate origin of Geomancy as an art. (Hence why she was originally planned for SoA's release, but was pushed off and then brought back for Rhapsodies. If I had to guess, I would imagine she was going to be tied to the relatively dropped plot of Rala Waterways being a constructed ley line.)

You also have super-gods like Altana and Promathia, and the embodiment of a cosmological principle like Atomos and "Mikaboshi" (Winds of Darkness or whatever the NM is called... it's Mikaboshi so I call it Mikaboshi).
And then you have Cait Sith... who is just tears. Why Altana cries kitties is because shut up.