As the name suggests, past-life therians are therians who identify as an animal/multiple animals because they believe they were this/these animal(s) in a past life. For example, my identity as a gray wolf stems from the fact that I believe I was a gray wolf before I was born into this life as a person and that the soul of the wolf whose body I inhabited still lies within this body I have now. From doing research, past-life therians seem to be the majority of therians.
Past-life therians are the therians you see with "kin memories" (I have a large amount). They have memories (vague or detailed) of their past life/lives as a nonhuman animal, be they memories as basic as fur pattern or as complex as domestic dog therians remembering what their humans called them. It's an amazing phenomenon.
Many non-therian otherkin also fall under the past-life umbrella as well. There are even non-otherkin that remember past lives as animals or humans or both.
There are ways to recover memories from past lives, but I will cover that in an entirely different book.
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Otherkinity And Therianthropy
Non-FictionA detailed guide on therians and otherkin as written by someone who is both.