I have never seen anyone write the term "Transgender X" it's always been "TransX" (Transman/Transwoman).
A transman is someone who was AFB (assigned female at birth) and is now living as a man, and a transwoman is someone who was AMB (assigned male at birth) and is now living as a woman.
Note: Living as. The legal status of this doesn't align correctly with the definition. For example, if we assume you are a transman; you live like a man, wear men's clothes, have changed your female name to something male (unless you had a unisex, you liked your female name, etc.), people refer to you he/his/him, BUT you haven't had GRS (gender realignment surgery) you, legally, are still a woman. Meaning although you are a man in all but hormones and genitals, you would still be treated like a woman in any legal system; e.g. you would get sent to the woman's ward of a prison, should you be imprisoned before you have had/started GRS.
HOWEVER. Transgender also extends to non-binary, though not through legal wording. A non-binary person is someone who doesn't fit nicely into "male" or "female" categories. Where a trans(wo)man fits into the male/female categories, the opposite of what they were assigned at birth, a non-binary person may feel in between male and female, or outside of it altogether.
Someone who identifies as androgyne will say that they are a little bit male, and a little bit female, in simple terms.
Someone who identifies as genderfluid will say that some days they are male, some days female, and some days they may be neither, in simple terms.
Someone who identifies as agender/neutrosis will say that they don't have a gender/don't identify as male/female, in simple terms.
And someone who identifies as genderqueer could be describe as any of the above, or one of the many other gender definitions that are out there.