I'm pretty sure furries have personalities (well, depending on how one represents them). Furries are the hardest to get under definition because it varies but going by your interpretation what I'd say differentiates a furry from those characters is that furries are generally people that like anthropomorphic characters and/or the fan characters made like them (and thus can be made with differing personality traits, characteristics, etc.). Characters established in video games, cartoons and the like aren't furries per se because they aren't fan characters, but are anthropomorphic characters nonetheless and furries can support those characters just as much, thus they do get attached to the fandom by fanbase.
And yes, there's a varying difference between characters even in the same medium, basically going from "Little Bit Beastly (human with animal traits)" to "Funny animal (animal with human traits)."
I think that's it... Well then, hope class was helpful today.