With all of these crazy -kin types popping up I feel the need to clarify a few things about my own beliefs and how they relate to this nonsense. I'm a little annoyed with all the strawmen and category-lumping I see.
Now, please hear me out here, before I start, please don't just read the following statement and jump on me for being another crazy fundie type:
I am a wolf therian. Now, hear me out for a minute here, please. What I believe isn't that complicated, and it isn't any more of a stretch than any other spiritual belief (and I know for a fact that not everyone here is an atheist). Essentially, I feel a deep connection to wolves to the point where I identify, not just with them, but as one. I know damn well I'm a human being, and it's actually really important that therians never forget that, it's really stressed in the more intelligent parts of the community. I'm not trying to make any stupid claims about how special I am or that I can P-shift** (nobody can, while it'd be awesome, that's stuck in the realm of fantasy), all I'm saying is that I, personally, have this belief and that it happens to be a very large part of my self identity.
Now, about accusations of appropriating the trans* movement or anything similar: I've never known any therians to do this, unless they're silly 14-year-olds who really don't know what they're talking about. I have NOT been discriminated against for being a therian in any meaningful way, I'm not being denied any rights as a therian, nor do I run the risk of being beaten up or straight-up murdered for it. If anyone does make a claim like that, I can tell you now that they are full of shit.
Therians, as a rule, generally have VERY little to do with otherkin. Even though we are technically a subset of otherkin, you're not going to find very many therians who will openly admit to this, and given the recent influx of... well, otakukin and similar, I now know why. But if you want to know something, most of us hate that shit, because it makes it hard for us to mind our own business identifying with actual animals that exist when there's a guy next door making stupid claims about being an alien or Naruto or a toaster, or all three, because why should anyone listen to us any more than NaruToaster?
Well, for me, at least, plausibility comes into play a little, as it's easier to say that you have the spirit of something that could plausibly even have a spirit, if you believe in such things in the first place. (There are a few attempts to explain therianthropy scientifically as well, placing it as a firmly mental thing, but I'm not going to go over the details here.)
As for the difference between therians and otherkin, therians are strictly animals that really exist, and otherkin believe that their soul (or whatever) is nonhuman in a more general sense, but the term is generally restricted to mythological creatures. Mythological, mind, not anime characters, certainly not specific ones. For people who believe in any kind of spirit world (as some people do) it's plausible that such mythological creatures could reside in such a world. Anime characters? No. Inanimate objects? Calling Poe's law on those ones. All of them. Or at least it started that way, started as parody before people started taking it seriously.
Oh, and if I ever hear a therian that I know say "check your privilege" I will punch them in the face, I swear, because as I said, we aren't being denied any rights, the most we ever get is mockery from people who have only heard of the crazy types and silly documentaries about "animal people". Oh, and that one episode of CSI, because we all know that's totally a good source of info on subcultures.
Getting back on track, I just want to reiterate that while I have my own problems with the community (namely 14 year old idiots and people who make stupid claims), I do want everyone to be aware that we're not all fundies about it, and please do not lump us all in the same category. I have this little belief about myself and who I am, and whether I'm right or wrong, it's certainly not hurting anybody. Having said that, the 14 year olds are likely to say things like "lol i hate humans" but that's just teenage misanthropy, I went through it too, they grow out of it. The ones who don't are generally yelled at or made fun of by the more intelligent members of the community anyway, because they make us all look like idiots.
So I don't expect everyone to just believe me, I don't want people to go around picking animals for themselves either, that's a mistake a lot of people make. Therianthropy by nature is a very personal thing, and it takes sometimes a long journey of personal discovery to realize it. The best way I can describe it is that it feels right somehow, like when I found out about it a lot of things in my life suddenly made sense. Am I trying to be a speshul snowflake? No, and I sincerely hope I don't come off as one, I just want to make clear that not all of us are nutbar.
So that's that, went on a little longer than I expected to. TL;DR: When I say I'm a wolf, I'm not referring to a character or a persona I've created for myself (I refuse to say "fursona") I'm simply talking about me. My inner wolf, you might say, who is not a separate entity, but an integral part of my identity. It's who I am, no more than that.
**physical shift.
*here's a footnote because I know you're looking for one.