Someone who identifies as Otherkin identifies with a human body and a non-human soul. As stated before, there are bad eggs that make it look like complete delusion, but you honestly get that in any group of people. Historically, there are mythos that speak of reincarnation and transformation, though there is no historical evidence of lore (that I know of) involving a human body and a non human soul, so this concept is a newer belief.
People who identify as Otherkin that have researched and have experiences with different kinds of spiritss do so through a gradual process and it isn't something you transform into. In fact, the term 'shifting' is attributed to both the Otherkin and Therian communities, but does not attribute to physical transformation, but more on the level of psychologocial, mental, and/or spiritual, depending on the beliefs of the Kin.
Another 'new' concept is called being Blooded or having spiritual ancestry. There actually is historical reference to this in lore and while the beings in lore are treated as physicaleings, they are not treated as physical beings by today's practitioners of these various paths. In lore, this references humans who have the ancestry of elves, Gods, Fae, and various other kinds of spirits. Personally, I've seen this a lot in Western European lore, though there could be more references in other areas I have not researched.