in a feminist context, "gender" has historically referred to externally imposed categorization and the internalization and performance of said categories. in a paper I wrote on this subject, I called this sense of the word "extrinsic gender"
"intrinsic gender," on the other hand, is what I used to refer to the sense of the word "gender" that a lot of trans people are talking about when they discuss social gender dysphoria and euphoria. it's the internal sense of category that's resistant to external impositions
but then we also use the word "gender" to refer to subconscious sex, which is the term Julia Serano coins in Whipping Girl to name the phenomenon we're talking about when we talk about bodily dysphoria. it is the "gender" being "affirmed" by gender affirming healthcare like HRT and bottom surgery
so, "gender" is: a social classing system, a performance, and at least two internal phenomena as well. and I really don't know if it's doing us a service to conflate all of these things!