Identity Dictionary

Generally, these identities follow the format of “trans___: one who identifies as / sees their true self as / wants to be ___.”

Transgender
When people are born, they are assigned a gender. Some people do not identify with the gender they were assigned - these people are transgender.
Many transition socially - they may start going by different pronouns, dressing differently, and going by another name. Many transition medically as well through hormone replacement therapy (HRT) and surgeries. None of these are necessary for being transgender. Neither is it all-or-nothing - many will choose some of these options but not others.
It is the most well-known transidentity. Most transgender people do not consider themselves a part of a larger transidentity community. However, many transID people see being transgender as one of their transidentities. Being transgender is seen by the community as a type of transID.

Transspecies
Transspecies folks identify as a different species than their current body's (human). It is similar to the experience of being otherkin or therian. A few transspecies folks have body modifications to look more like their species. Many transspecies individuals will use accessories and behaviors to feel more close to their species.

Transage
Transage identify as an age different than the one they are chronologically. They can be older-to-younger, younger-to-older, ageless, agefluid, or agevague.
There is a stereotype that all transage people are predators lying about being older-to-younger. Despite what a 4chan trolling campaign (clovergender) might be trying to tell you, being transage is no excuse for abuse. .
Transage people may alleviate dysphoria by dressing different, acting differently, or changing their bodies. One example is shaving or not shaving. They might dress like a different age group.
Diaracial (or transracial)
Diaracial is the alternative name of transracial. The prefix dia- is used as an alternative for trans-. It is preferred by some because the word transracial is already being used by transracial adoptees.
Race is a classification of human beings based on apparent traits and ancestry. Diaracial people identify as a race they would otherwise not be considered a part of. It also applies to people who are mixed race and want to be monoracial (not mixed), for example. Though they are generally stereotyped as White to Black or White to Japanese, there are many diaracial people who do not fit this experience. Many are people of color by their genetics. Many are transWhite or aracial. A diaracial individual may also identify as transethnic or diaethnic/diethnic.
Diaracial people may transition by changing their name and coming out. Sometimes, a diaracial person will transition by skin darkening or whitening, changing their hair texture, or through surgeries to change their facial features. Another common experience is researching and learning more about the culture. As misconceptions can be very harmful, it's good to learn about cultures outside of one's own.
Here is a small study I read once on the subject.

Transabled
Transabled people identify with different abilities than what their body currently has. In this context, it is usually less abilities. It includes Body Integrity Identity Disorder (BIID) and xenomelia. Many experience the desire to have a limb amputated or paralyzed. They might feel as if the limb is alien and should not be there. Some transabled/BIID people have reported a dramatically positive change in their lives after amputating their desired limb, however as far as the studies I have read, I cannot accurately tell the rate of regret for these percedures. Outside of limb-focused transability, some want other changes to their body that would be considered disabilities. Other ways to transition include getting aids - though it is important to keep in mind if doing so would prevent others from using the same aids, such as if they are in very limited supply.
Here are the studies I have personally read so far: [1], [2]

And everyone else...
Outside of these, there are still many other experiences, far too many to name. Many overlap, and lots of people identify with several of these identities.