While there are trends in terms of species identity, the actual difference between the communities lies in their origins and cultural nuances. In both groups, there have been always both people who have identified as animals and as non-animals.
Otherkin has its roots in feminist neopagan spirituality and historically tended to focus more on past life memories and purpose in a human body.
Therianthropy originated on Usenet (kind of like an old forum) and historically tended to focus more on dealing with things like shifting, instincts, and species dysphoria.
Of course, that's not to say that every otherkin individual or every therian subscribes to those particulars. Rather, they are simply the historical context. You should, of course, choose which community/ies is/are right for you based on your current experiences of them.
For more on the communities' origins and histories, see:
"Otherkin Timeline" by Orion Scribner
"A Timeline of the Therianthrope Community" by House of Chimeras
For more on cultural differences, see:
"Therians and Otherkin Don't Have Exactly the Same Experiences" by Rook
"You are the sum of your friends" by mord
For more on what kinds of theriotypes have been present in the therian community, see "Therian: Dispelling the Earthen Animal Myth" by the River System: