When a person does not identify AS a non-human animal but instead has a strong "connection with" or feels a "relation with" an animal. "I identify WITH wolves." does not have the same meaning as "I identify AS a wolf." Being a Therian is more than "really liking" an animal. Liking a creature a lot does not equal an identity as that creature.
To use the term correctly, a person who feels close to deer would say, "I am deer-hearted."
The equivalent term in the Otherkin community is other-hearted.