Taking from the userinfo of the therianthropy community, "therianthropy is a state of being/philosophy/condition/etc. in which a person identifies in some way as a nonhuman, Earthly animal." Therians feel (some wholly, some in part) that they ARE an animal, which is very different than the totem concept of having an animal spirit as an external guide. I feel therian, in a sense, but I don't think that being 'therian' is something that only certain people are, which most therians seem to believe (from the little that I have read). I also do not interpret the thing I believe in a broad sense as 'identifying,' and I don't see it as an animal spirit trapped in a human body/mind (both of which are beliefs of SOME therians, not all). Those are fine beliefs of course, they're just not the thing that I believe, which I call spirit-shapes.
I personally believe that all people have more than one spirit-shape, but most people are unaware of this. By spirit-shape I mean a shape/awareness which the spirit can shift into; I think all people have both a human spirit-shape which looks very like their body (sometimes with wings), and at least one animal shape. I think that when a person shifts their spirit-shape, they are in a very real sense shifting into another form, even if it doesn't look different on the outside. I've seen people spirit-shift and whoa, is that an intense thing to witness (especially if they are a predator shape, heh). The eyes, mannerisms, and instincts change -- but most of all, I feel the presence of the animal that they are. I think that some people feel this as an intense identifying with a certain animal, but when it is allowed to assert itself freely, it becomes more than that; the difference between having a favorite animal and BEING that animal. I think your favorite animal(s) can give you a clue as to what spirit shape(s) you may have, but it's a completely different concept. I also think that so-called 'mythical' animals (dragons, unicorns...) and humanoid creatures (fae, merfolk...) can be spirit-shapes.
I also believe in totems; I believe that certain animals will appear in your life when you need a message from the universe. Sometimes these might be lifelong guides for you, and sometimes it might be a one-time visit, but their purpose is to bring you wisdom. They might come to you in a dream, you might see them outdoors, or you may even see them repeatedly as decorations. A lifelong totem differs from a spirit-shape in that it is an external guide rather than a part of your being; though you can identify with them in the same sense that people identify with the Deity(-ies) or spiritual leader(s) they follow.
I've started my post on my own spirit-shapes and totems, and it's turning out to be quite lengthy so I'm going to post this on its own first. (I'm also going to gather photos -- I'll probably end up posting that this evening)