There really is no established Therian symbol. However, there is a symbol that is generally accepted as the Therian symbol.
"The Therian Symbol was created by members on The Werelist a while ago. The intent was to make a universal therian symbol for the entire community. Most of them adapted the basic design (a Greek theta symbol interwoven with a delta) into a unique charm with personal significance to them. Those therians began calling the symbol by a specific name, which seems to fit its Greek origins- therios." - Therian Wiki and also,
"The Theta Delta is believed to have origionated from an early incarnation of The Werelist, where it was decided on in a forum topic that revolved around the creation of such a symbol. The Theta Delta was created, Theta, being a T, used to represent the word "Therian" and Delta for a change, as in a shift."-Therian Wiki
Some Therians prefer to use their own symbol and others prefer no symbol at all. All in all it's your choice to pick a symbol that defines Therianthropy to you.
Often times Therians can Shift into different forms; Some prefer to stick to one and other tends to Shift between forms. The image underneath shows a scale of where you are mentally and how you see yourself spiritually, red represents the human or physical side, and the blue represents your Therian side. The green dot is where you are at in the form. We get these forms (other then fully feral) when our physical conscience combines with our Therian side during Shifts.
There can be many different forms, but these are the most known, and these are the forms used frequently throughout history. Many of you are familiar with the gods and goddesses of Egypt, in which the human and Therian headed can be found.
There are many different types of Therians; the most common are the ones who Shift into one animal. There are people who believe they are Therians and don't Shift at all. Some even believe they can Shift into more then one different species.
Standard Therian: Someone who only Shifts into one animal, or one type of animal.
PolyTherian: Someone who believes they can Shift into more then one animal, often two or three.
AnTherians: Animals that shift into other animals or humans, they experiance many of the same things we do, and can be polytherians, or nonshifting Therians themselves.
Nonshifting Therian: A Therian who has memories of being an animal, but cannot Shift at all.
Con-Therian: Someone who believes he or she is constantly Shifted.
Therians are earthen, anything that ranges from a bug to a blue whale. Extinct animals like mammoths, sabertooths, and dinosaurs can also be therians. Anything that lives or has lived on earth is what therians associate themselves with. Otherkins are beyond earth creatures, including mythical creatures. Otherkins claim to be dragons, fairys, griffins, aliens, etc.
Something that confuses people is the practice of spiritual shapeshifting also known as spirit borrowing. Shamanism is known for this, they use their power animal or totem for help. These people can mentally shift into an animal's spirit to learn a lesson, or use the animals’ power. This is different than Therianthropy because therians feel they are the animal, and spirit borrowing is asking to be lent the power of an animal (which normally induces similar feelings to therianthropy, feeling like the animal and such). Therians can practice spiritual shape shifting too, but if they are trying to borrow the spirit or an animal, it can sometimes prove a little more difficult. For example, I am a wolf therian, I do not have to borrow a wolf spirit, but if I wanted to shift into another animal (like a cat or bird) I'd have to borrow that spirit and it could be a bit more difficult. For Therians their inner animal is who they are, and people who practice spiritual shapeshifting just borrow spirits to Shift and learn lessons. It's a tough subject to explain, but if you study more into shamanism you will see the difference.
Although this is based on spiritual therianthropy (which is the most commonly believed) there are people who believe it is more of a logical matter then spiritual.
Spiritual therianthropy is the most common among the therian society. They believe that they are a therianthrope because of a spiritual reason, having to do with spirits/souls, reincarnation, and the astral world.
Logical therianthropy is more of a scientific view of therianthropy. Those who believe they are this way because of some kind of psychological incident that was damaging or just the complexity of the human brain in general. Most people who believe that therianthropy is a logical thing have their own reason and story why.
Common Theories of Spiritual Therians
Here are some theories of spiritual therianthropy.
Common Theories of Logical Therians
Here are some theories of logical therianthropy
Both Spiritual & Logical
There are people who believe it is both a spiritual and a logical situation. For example, some believe that having identity crises allows them to spiritually connect with the animal.
Therians are often confused for furries, however there is a huge difference between the two.
It is not too common but some therians join furry communities and get involved with the furry fandom. Therians are not likely to wear costumes but don’t be surprised to find some wearing tails or masks.
Religion has no significance to therianthropy; they are two completely different subjects. But do not be alarmed if you find therians who gladly incorporate therianthropy into their religions or ceremonies.