And what distinguishes those things besides physical form and function?

Gender isn't a spectrum, there are two genders (which are, despite what leftists claim, the same thing as sexes) and those are (1) male and (2) female. When you are born as a male, you have xy chromosomes, and if you are born female, you have two identical chromosomes "xx". Every cell in your body is built based upon that genetic information, meaning that as you develop, every fibre of your being is literally built programmed "male," or "female." Just mutilating yourself and doing hormone therapy cannot change your sex/gender, as every single cell in your body is preprogrammed male or female. All you can do is make yourself an incredibly ugly male. or female, it's impossible to "change" genders.