Trans people that transition do not do that to assume the opposite gender (at least as Gender is used today especially in the same circles), they are attempting to assume the primary secondary sexual characteristics of the opposite sex.
I never got a good explanation why transsexual was changed to transgender other than the fact that you can’t change your biological sex.
The whole sex vs gender debate is a literal mess. On one hand gender is a social construct if so transgenderism would never be an issue, if gender is so fluid and a “choice” then why convention therapy can’t work (I don’t think it can, and I also don’t think that gender / sexual orientation is particularly fluid or a choice).
Personally I started to look at sex or well sexuality as the social construct these days, it’s clearly a tool to form societal structures as seen in places like prisons for example.
Gender on the other hand for me is the heuristics that arise from biological constraints due to the (biological) sexual dimorphism of humans.
As far as “black” vs “African American” that seems to be an utterly American thing.
In the U.K. Black British for example is literally an acceptable way to call a black person, if they are black British that is since there are plenty of other black minorities in the U.K. like black Caribbean etc. I’ve never seen anyone saying African British.