Quote 引用元：Rawrz 投稿を閲覧
The others, like Bahamut are probaby astral/Umbral.

Bahamut: Astral Fire
Odin: Umbral
Moogle mog: Astral

Etc
Small correction, I think it was explicitly stated in the lorebook that Bahamut was all elements astrally aspected. That presumably means Shinryu would be the same, though maybe umbrally aspected.