I have heard from a Therian I know that therians are basically animals from what may as well be called "our world" AKA the "real" world, while otherkin can include dragons, elves, and so on. An otherkin I met told me that therians are basically otherkin who stick to our-world animals, and an otherkin might be something like a dragon, but they aren't limited to that. I think there's probably more than one definition out there, but there seems to be some consistency: therians identify as animals that you might see walking around on Earth.
In my experience, that is pretty much correct.
The general stance is that therians are those with similar thoughts, beliefs, and experiences such as totems, guides, reincarnation, phantom shifts/sensations, dreams, etc. regarding earthly animals, which can range from casual conceptualization, to solid defining beliefs.
There are also some therians
out there that go to extremes and insist that they actually are (not just feel like they are or were, but insist they literally are) a certain animal, making claims of physical shifts, or even having special powers, abilities, etc.
The majority of therians regard such things as "fluff", and don't take such individuals very seriously at all.
Otherkin to my understanding is basically the same thing with the same stances, only involving mythical and otherworldly creatures and entities.