History of Feminism

sex is biological (but not necessarily binary; see here).

Gender identity is the personal and subjective sense of "maleness" or "femaleness". This personal and subjective sense of gender identity is not related to gender roles or to gender performance, both of which are social constructions. Most research indicates that gender identity is formed by age three or so; some relatively small number of people (anywhere from a fraction of a percent to 1%, apparently) experience a subjective disconnect between their socially assigned gender role and their internal gender identity, which frequently results in their engaging in the performative aspects of that gender identity specific to their culture. This is not a new thing; transgender people (as we now call them) have probably existed for as long as humans have existed (see historical examples like the Chevalier d'Eon, and non-Western examples like Indian hijras and Native American "two-spirit" people). And there's a growing body of research that indicates that gender dysphoria may have a biological/neurological basis.