Deusphages are a type of variation that some Aragami subspecies present to their original species, just like Fallen species. Most of the Deusphage species either use the Divine element or are weak to it (or both at the same time), and all of them are named after gods of either Greek or Japanese mythologies. Deusphage species are divided into two types, named Type 1 and Type 2: Type 1 Deusphages are named after Japanese gods, while Type 2 Deusphages are named after Greek gods.
This is a comprehensive list of the Deusphages and their original species for comparison purposes.
Deusphage is an amalgamation (a combination) of words from different cultures. "Deus" means God in Latin, while "phagein" means "to devour" in Greek. In the literal sense, Deusphage is "to devour a god", or, in a simpler term, a "God Devourer". According to Norn Database, they are God Eater Devourers. As God Eaters play the role of the hunters against the Aragami, Deusphages play the role of the hunters against the God Eaters themselves, so, to sum it up, they are extreme "evolutions" of normal Aragami that happen in order to counteract the actions of the God Eaters.
While Type 1 Deusphages have differences when compared to their non-Deusphage counterpart, Type 2 Deusphages are simply recolored versions of a certain Aragami's variation (e.g. a Zeus is simply a recolored Aether). Their materials are used to craft collaboration content exclusive to God Eater Burst, and therefore Type 2 Deusphages do not appear in any of the other God Eater games.