Welcome, here I will be explaining different types of therians, so lets start with what a therian is.
A Therian is someone who identifies as an animal that once has, or still does, walk upon Earth. Now that you know what a therian is, I well touch on what a subcategory is before moving on to a main one. A subcategory of therianthropy would be something that describes a group of theriotypes, one example being the Paleotherian. Paleotherian are therian who identify as a creature that is extinct, such as a type of dinosaur or mammoth. Even if a closely related species of the creature is still alive and thriving, if the species is extinct, the therian is a paleotherian. Paleotherian aren't as common as other genres, and aren't that well-known as a result. Now I will move onto bigger categories of Therianthropy.
Someone who identifies as a single earthly animal, and can have various experiences around this type, including mental or phantom shifts. The "typical" therian.
A therian possessing multiple theriotypes at the same time, and can experience anything possible for each of them. Some of these types may appear more important than others, but it's not always the case.
A therian who does not experience shifts under any condition, but still identifies as non-human through other means.
A kind of nonshifting therian that has similar experiences as other therians but who do not shift- rather, they are constantly shifted into an animal state, with no variation.
A kind of therian who, similarly to the contherian, constantly experiences this nonhuman side and do not experience mental shifts; however, they can experience changes on a sliding scale, or combinations between human and animal mindsets, but generally in a manner that is not as extreme as with shifters. Also called "vacillant".
A therian who's theriotype is not one specific sub-species. For example, rather than a tiger specifically, they encompass all felines or a "clade". It is not a temporary or placeholder label for those who are uncertain or haven't yet narrowed down their species. A cladotherian does not think such a narrowing of species is possible or applicable for themselves.
A therian who's thereotype is not found on earth, also known as being mythological. otherkin is the term usually used for this, but some still label over therian. ( Description is thanks to @Alliana
These are the types of therians,and now I will talk about psychological therians and spirtual therians, two different types.
A psychological therian is someone who feels their identity is a result of a neurological abnormality or is a part of their personality. They do not feel that their identity has any correlation to a past life, but rather their identity is the result of who they are as a person in this life, on an emotional or psychological level.
A spiritual therian is someone who feels their identity is a result of spiritual attachment and interconnectedness on an ethereal level. They believe that their identity is formulated as a result of reincarnation, soul misplacement, or another means where they feel they are this being on a spiritual level. They do not feel that their identity is due to any neurological or (generally) personality related factors.
Thank you for reading this post! Feel free to let me know if I missed anything!