Personal theory of sex and gender, probably cn for trans things and identity stuff. I'm not sure how robust/coherent this is, I've not tested it anywhere else yet.
I think gender has been conflated with sex and broadened to the point that it's basically useless. It was invented in the 1950s as a way to separate masculine and feminine from a person's sex, so that we could talk about the expectations we have of each sex separately from said sex--so that we could discuss gender roles.
However, instead of liberating us from gender roles, we have merely tried to broaden the definition of each gender to the extent that "man" and "woman" now don't have any meaning. We say that the gender woman is still a woman no matter if she's in frills or if she's in a mudpit. There's nothing coherent about such a broad definition except to say that those women are females, are of the same sex. Gender has nothing to do with it anymore once you've made the category that big.
I don't think there's really any point to saying "she's still a woman" unless you're trying to invoke the things that women get access to: marriage, respect, etc. Those were the important things to women at the time that "gender" became a thing. Same for men: it was important that a feminine man still be a "man", so he could find a wife and be respected. It was not acceptable to deviate from that "gender", from that sex.
I think that's what gender has come to mean today: nothing but a synonym for sex, exactly what it was before it was invented. We've not liberated anyone, we've merely changed the fence from sex to gender. There's still things that each sex can't do, even though each can use many kinds of gender expression (masculine, feminine).
What I think may help is to give gender a real definition of its own, and to invent/label the other sexes and genders that exist. Two-party systems seem to be as bad for gender and sex as they are for politics. Although things are being invented for gender, and few are taking that well: "special snowflakes" is how they're laughed off. Sigh.
As for the definition of gender, I don't think calling it "the interplay between masculine and feminine" makes much sense when we've pretty much eroded everything that means, in calling a feminine male still a man and a feminine woman still a woman--both are feminine, surely they ought to both go by the same gender label? It seems that gender takes account of a person's genitals, not just their masculine/feminine socialization. If we go with that, then gender ought to be sex+sex socialization.
So then, you get people who chafe against their socialization, who accept it, and people who think they should have been in the other class (for example). People who chafe and are female would be butch, people who accept and are female would be cis woman, and people who think they should have been in the other class and are female are the trans men. I'd put the male ones here but I don't know the term for feminine males. I don't know if sexual orientation would throw another angle into these labels, making it three-axis instead of two. Frankly I don't think genitals ought to matter to gender (even if it does matter to sexual orientation), but society insists that it be part of it.
I think it's a bit odd that we yank out certain personality characteristics and call them "gender", but we give arbitrary importance to a lot of other seemingly pointless things too, so this isn't that unique a thing.