Are you one?

So what exactly is "transgender"?  Donald Trump has said that transgender people cannot serve in any capacity in the U.S. military, but my (perhaps imperfect) understanding is that transgender people are those who feel their physical body does not reflect their true gender.  In other words it is those who feel they are trapped in the wrong sort of body, sex-wise.  The point I make is that this is essentially a mental thing - so how are you going to identify them, if they don't wish to be identified?