The differences between a human and a 'kin are primarily mental, as most if not all otherkin are spiritual nonhumans inhabiting a human body. The specifics will vary depending on what metaphysical model you subscribe to, but there are a few permeating traits. While these are usually present in otherkin, having them does not necessarily make you 'kin.
Memories: Otherkin who are {{Reincarnates}}, {{Walk-ins}}, or change themselves by invoking specific spirits rather than the general essence of a critter may have access to the memories they had in their other incarnation or body. See PastLifeMemories
Body Sense: Your sense, somewhat tactile in nature, of where your body parts are and should be. Just like a person who lost an arm can have a phantom limb effect and a transsexual can have a bizarre sense of needing to be in a different body, an otherkin will often feel phantom wings, tails, whatever. One's astral body is shaped at will by thier imagination, but when they are paying no attention to controlling it it will revert to what they think they look like which will include any phantom limbs. A person's mismatched body sense will be plainly visible to astral senses.
Instincts: Conscious or subconscious memories and body senses will give you reflexes that just don't fit the normal human pattern. This includes mimicking the personality of your species, avoiding hitting people with your wings, being sexually attracted to nonhumans, and maybe even (woe is you) trying to breathe fire on someone in the middle of a fight. Traits like this will appear in _everyone_ as regular personality quirks, so although they are present in most 'kin, this is one of the most unreliable ways to claim what species you are.
-Suigin Flair