When in doubt, just use the literal definitions of the parts of complex words...
trans = across / switched
gender = what a person personally identifies as
sex = what a person is physically identified as
Transgender thus applies to anyone who identifies as a different gender than what is standard for their sex chromosomes, even if they have not undergone any sex-reassignment surgeries/treatments.
Transsexual applies only to those who have physically altered their bodies to appear as the opposite sex.
All transsexuals are transgenders, but not all transgenders are transsexuals.
Just like all apples are fruits, but not all fruits are apples.
... Also maybe I should be reconsidering using "fruits" as an example, given the context.
TL;DR: Transsexual
is the correct tag here, since it's more specific.