Gryphons are, in mythical terms, unique beasts, with the head, wings and 'forelegs' of an eagle or large bird of prey and the legs and body of a lion. In more recent and broader terms, it now refers to almost any slicing of any specie of feline and any specie of bird.
In therianthropic terms, if one has a gryphon animal side, it can mean one of several things. They can view their animalside as being single specie, a mythical gryphon, with feline and bird traits, but also something entirely new among the merge of creatures. Another possibility is that a polytherianthrope with two animalsides, one of a bird and one of feline, call themselves a gryphon for convenience, while maintaining that the two creatures are still separate species within them. There can be various levels of these two group, polytherians whom experience shifts that feel as if their animalside is in the form of a mythical gryphon, or gryphon therians whom experience separate bird and feline shifts.