Drilling further into research on therians, otherkin, and the difference between them, I've finally seemingly come up with some answers regarding definition, and what those are and aren't. I think.*
Whether on a spiritual, or metaphorical, or whatever kind of plain, both regard their souls as being... different, from normal people's. Like being transgendered, only this is more transspecies -- though those who believe that their souls literally aren't human are few and far between, and who knows, maybe even those guys are just, starved for attention, or something. (Maybe not, but, maybe. Lots of people believe lots of things.) So, really, no, I guess it's nothing like being transgendered. But, yeah, exactly like that.
What we're talking about are therianthropes and otherkin. I've mentioned how interchanged the terms are, and how I don't believe they refer to precisely technically the same thing, and how I'm probably right because they're really not precisely technically the same thing. There are some great resources to look into this kind of thing, though, and how it looks so far: therians are more, souls-of-animals, people, while otherkin are souls-of-mythical-and-legendary-races-and-stuff kind of people. Blurry lines still, especially when dealing with dragons, and you do see a lot of intercourse between the (fandoms? subcultures? countercultures?)... but it's all wholly distinct from space aliens. Which is good to know.