I've got a bit of an odd way of looking at it. I guess it's a scale of anthropomorphism interest. It starts with those who like the basic idea of anthropomorphism, stuff like stone golems, trents, the homunculus from FMA. Human features on non-human things.
Then yah move onto light animal based anthropomorphism, or the "I'm not a furry because I just like cat-girls" crowd. Pretty self explanatory.
Next is interest in animal based anthropomorphism from an aesthetic stand point. No sexual interests what so ever. A great example is Lackadaisy Cats, were all the characters are anthropomorphic cats because the artist feels that they convey better expressions, and they do!
After that is what people normally think of as a "Furry", though I refuse to call them that. Same as above except they do have a sexual interest as well. This is where things like anthro-personas and mild to intense explicit content with all the bog standard fetishes (feet, large/small breasts, BDSM, and so on) come into play. "Stage performance" fur-suits are in this section too. I consider myself between this category and the last.
Then come the people I despise. This is my definition of the word Furry. Anyone who partakes in one or more of the following: Devoting a majority of their time creating, purchasing or view explicit content, un-ironic use of "furry words" (yiff, purring/barking, using animal parts or terminology instead of human, murr, that whole deal), extreme fetishes, sexual use of a "fur-suit", calling a significant other "mate", multiple set of the same genitalia, and getting huffy about "fursecution"
And lastly there are those who take it even farther. Those are they kind that legitimately believe it's a lifestyle and should be unconditionally respected, believe that the "Fandom" is a coherent group that can "push people out", believe they actually are an animal in a human's body, systematic liars and massive creeps, god-complexed "furry police", and the hyper-drama mongers and mentally detatched/deranged that will go far enough to threaten legal action/DMCA over petty things. These types also suffer the symptoms of the previous group.