I haven't done extensive research on the topics, but I want to make a distinction that's rarely mentioned. Therianthropy is a spiritual connection to a certain animal, or possibly several. This CAN INCLUDE "mythological" beasts, like dragons, griffins, and so on. Otherkin feel they are something else. If you're spiritually connected to cats, you're a therian. If you feel you ARE part cat, whether in spirit, body, or mind, you're Otherkin. If both, then both. I'm personally a furry, a therian with several theriotypes, and Otherkin. Think of it like this. If a therioshift is permanent, you're probably Otherkin. For example, I'm a cat through and through. People I don't even know will tell me I move, act, and react like a cat. A coworker once called me Felix the Cat because one day he heard purring and ran around looking for a cat until he realized it was coming from me. I don't control that; it's just the way I am.
On the subject of Empaths, I'm not sure most people know what we are. It's hard to find stuff on our kind, and a lot of us never know. An Empath is someone with a hyperacute sensitivity to the emotional conditions of those around them, to the point of literally feeling the emotions of those people as if they were their own. Once an Empath figures out what they are, they can limit that ability. If they don't, they're bombarded with overwhelming amounts of emotions they can't make sense of. It's extremely uncomfortable. That's an understatement really... Imagine the ability to hear thoughts, but you can't turn it off. The thoughts of everyone in the vicinity pass through your head. That, but emotions.