There's also genetic "oopsie-daisies" born with reproductive organs of both sexes that are scientifically neither/nor (THAT'S technically where science is settled). They generally "identify" as the gender they physically match the most or have surgery to remove the oddballs, pun intended.
Trans people are the people that (depending on who you ask) decide they want to be the opposing gender. While that's genetically impossible, they can at least look/feel the part, through dramatic surgery and hormone therapy, though unfortunately they'll never be the gender they wanted to be. It's only a physically/aesthetic change.
It doesn't stretch any further than that, unless your a SJW, or course; if you're a SJW you can flip-flop genders 60 times a day and if anyone disagrees with you it's transphobia and you're evil and need to die so the gender-fluid pan-demi-asexual otherkin can be free.