-Furries wear animal costumes...
Not necessarily. A lot of furs don't even own a fursuit. And there is nothing about furry that requires that you need to, or that you even want to. The only thing that furry implies is that you have an affinity for anthropomorphic animals. This could take the form of costumes, but it could also take the form of artwork, stories, or other things.
-Furry has a sexual side, therianthropy really doesn't
While I'm no expert on therianthropy, I would bet there there IS a sexual side. People are inherently sexual beings (which helps keeps the species going) and so pretty much anything they get involved with is going to have a sexual side. Plus, there are plenty of erotic pictures and stories that focus on transformations and such that would seem to be more in line with therianthropy than furry. Plus like Avan said, there is a lot of overlap.
-Furries may have multiple personal avatar characters, therians identify with a specific species or subspecies of animal
A lot of furries identify with a specific species or subspecies of animal. For example, my fursona is a red fox and I don't see that ever changing. Unless you are trying to say that therians cannot possibly identify with more than one species. As I said, I'm no expert on therianthropy, but I doubt that's the case.
-Therianthropy has spiritual connotations and is often intertwined with spiritual beliefs, furry is just a fandom
I think this is probably the most definitive difference here. However there is still a lot of overlap. For example, there are plenty of furs that wouldn't be happy with the claim that "it's just a fandom" or the implied claim that furry can't be spiritual. (It's not for me, but then I'm not "spiritual". I've found that "spiritual" is either so ill defined that it's nearly meaningless or else it's definition doesn't match with reality.)
-Furries (in general) tend to see therians as role-players who have taken their role too far, while therians (in general) tend to see furry as a lighter version of therianthropy.
I would mostly agree with this. Though I don't know I'd use the word "role-players".
My personal opinion of therianthopy, as well as that of furs that think they are not really human, is that they are out of touch with reality, at least on this issue. I mean no disrespect to anyone, but I've seen no evidence that supports it being any more than a delusion.