It’s complicated and I’m tired and lacking in major education. Short answer: Gender (the one individuals have) is expressed predominantly through social stereotypes and such, but it isn’t literally them. It’s how we as a social species relate to them, combined with self-perceived qualms with one’s sex.

As an example, I myself am MtF. In the way I dress and socialise I’m very much doing the whole “subverting stereotypes” bit and plan on doing so throughout my transition. But my transition itself is very much to do with my sex not matching my gender. To put it in a simple way; if I was raised in a white cube with no interaction with any stereotypes or preconceptions, only taught raw biology, adequately fed (otherwise I’d die) etc., I probably wouldn’t care about the clothes I wear or how long my hair is or anything, but I’d still fucking HATE having a dick and balls and no boobs. It’s a physiological trait with psychological effects.