Both the physical and spiritual animals are called familiars. The physical tends to be just called a familiar (animal) whilst the spiritual animal can go by many names; such as but not limited to familiar spirit, totem animal, totem spirit, fylgja, fetch, and spirit animal.
The physical familiar is an animal that you feel closely connected to. They tend be present in (magickal) workings and can aid in these workings by adding energy. These can be pets, but are not always pets. Some can be wild.
The spiritual familiar is one that you connect to in a similar yet different way. You connect with the spirit because, in a sense, it is part of you. It's connected to you by your spirit. So in a sense it is you - kind of like a small part of you that has taken an independent form of it's own. These familiars can take on any form that they please. They may take on the symbolic and/or spiritual manifestation of an animal that you are connected to. - in the spiritual/symbolic aspect. They may take the form of an animal that you feel comfortable with. They are not limited to only animal forms. They can take on hybrid/mythological farms; human-like forms; may even take form to look just like you do; etc. But it is not uncommon for them to stay in one form. They can help in a wide range of spiritual practices. Such as journeying, faring-forth, pathwalking, astral projection, etc. They can be used for guidance; and maybe councilling. It is not uncommon for the person to take on the for of his/her fetch when doing said spiritual workings. The familiar can be a mediator in the sense that they can send and relay messages.
With either type of familiar you are not limited to just a single familiar. You can have multiples of either one.