As what others said, anthropomorphic and zoomorphic characters predated the furry scene. The furry scene is based on these kinds of characters but as a genre and aesthetic, there are two kinds of furry. Gateway drug furry is anything with an animal or animal like character that’s created by non-furries, something like Thundercats and Looney Tunes. Whatever is furry is up to anybody else’s guess and also dependent on the way said character’s depicted (Tigra’s* practically a grey area depending on whoever draws her at all).
To be fair, kemonomimi/animal ears aesthetic is also a grey area in that it could either convert somebody to furrydom or be a socially acceptable furry given the stigma. If Killing Bites is any indication, people can and do use this to push the upper limits of the uncanny valley without being too furry for some characters though some are outrightly furry. Killing Bites and the like (including this comic that gets posted on 4Chan threads about it) are firmly in this grey area given the way they do with human-animal hybrid anatomy.
Actually so is Thundercats when you think about it. Then there’s subculture furry which only appeals to those in the know. The characters are animal-headed with humanoid bodies but sometimes with digitigrade feet (even one furry suggested that they should be plantigrade given they tend to be bipedal) though relatively more humanoid characters are acceptable. It’s practically analogous to bands that can make a goth/metalhead out of somebody and those firmly entrenched in those scenes.
The former is whatever it could be and lead somebody to, the latter is what it is.
*There’s legitimate furry fanart of her.