My opinions on here are unpopular, but I see it as gender and sex are interchangeable synonyms. You're either XX or XY. I'm not going to bring up intersex because we aren't going to use sexual development disorders and mishaps to suit our needs here. Gender identity is the correct term.

Gender dysphoria is a mental illness, that causes one the unease and hatred of one's own sexual characteristics. It isn't about behaviors (though many may act what is stereotypically pinned as male or female). There is stigma behind mental illness, which perhaps is why this idea is rejected. Either way it is in the DSM, which relates to mental health. It's there for a reason. It's an identity disorder.

The treatment for this is the changing of sexual characteristics via HRT. It puts the sufferer at ease with use of the opposite or neutral pronouns. It depends if they just dislike their sexual characteristics, or feel the need for the opposite. This is gender identity - how you feel about the sex of your body, and how you feel it should be. A completely physical experience.

Which also brings us to the fact that you can't be medically transgender without experiencing gender dysphoria.