I think that gender largely overlaps with biological sex, almost all of the time. It's an inextricable part of it for the majority of people. It's not a conscious choice we make based on perceived preferences, it's just who we are. To a very, very large degree, one gives rise to the other. However, I do think that gender is a bit of a spectrum and it's not quite as straightforward for everyone as it is for most.
I get that some people completely reject gender as a natural phenomenon, preferring to think that it is purely a social construct, there is absolutely no difference between the male and female brain and that our hormones and chromosomes have no bearing on the gendered character traits we end up with, but I strongly disagree. It's scientifically proven that, in the most general terms, women are better at certain things than men, and vice versa, because we've been bioligically designed to be that way. I'm all for telling kids that there is no such thing as a gendered role, they can do any job or play any sport they like, or play with whatever toys they like, regardless of their sex. But the fact is that, over and over again, it's proven that while children of both sexes will dabble in all sorts of activities to an extent, boys will overwhelmingly end up gravitating towards, and excelling at certain things more readily than girls and vice versa.
The fact that so many more women end up pursuing careers like teaching, nursing, childcare or social work than men, and so many more men gravitate towards the armed forces, engineering, mechanics, physical trades or careers using STEM subjects is not accidental, nor is it purely as a result of social conditioning. Social conditioning only plays a part because we've developed certain expecations based on biology.
I often watch young children playing and interacting and notice a marked difference in the way that most (not all) children of one sex will behave compared to the other. Little boys are, in general, much more physical and fidgety. They will chase one another, playfight, try to trip one another up and find this hilarious, constantly battling for physical dominance over one another in a way that most little girls simply don't. And if they did, it would be perceived not as fun, but as an act of aggression. It would bewilder most girls to be faced with this behaviour constantly from other girls, but for boys it seems par for the course. Boys tend to find their humour in different things as well. Again, it's a massive generalisation, but girls are cats, boys are dogs. I'm sure anyone who is a teacher of primary aged children will have observed this too.
Not all people are going to strongly identify with the all, or even most of the classic gendered traits that match their sex. I suspect that is down to hormone level differences and various other complex factors. Hence why we have always had the stereotypical tomboy, or whatever the male equivalent of that would be called. Although I'm struggling to think of a term that doesn't sound homophobic or pejorative for a boy? Which is funny when you think about it. No-one ever sees the term tomboy for a girl as offensive, or necessarily suggesting she's a lesbian. If anything it has always been said with a hint of admiration and an indulgent eye roll. It describes a robust, no-nonsense girl who is physically bold and brave and doesn't waste time or energy on trying to make herself look pretty for other people. Whereas a boy that displays more stereotypically feminine interests and qualities is often seen as a bit of a weakling and a 'fairy' in old fashioned parlance.
I do get that so much about gender stereroyping is the result of social conditioning, but it's not entirely due to that. The social conditioning didn't come first, the biology did. What we observed over millenia would almost certainly follow in girls and in boys as they grew up, in terms of gendered behaviour, was because it was innate. So the rest was then largely assumed and woe betide anyone who didn't fit the mould.
I don't think that if a girl wants to rough and tumble, play contact sports, reject pink and frills, swagger and 'manspread' like a boy instead of tippy-toeing and twirling like a girl, that it's evidence that she was actually meant to be a boy. By the same token, if a boy wants to sit quietly, learn to crochet, play with dolls, use his mum's make up and shies away from rough and tumble play, it doesn't make him a girl. It simply makes him a boy who is very in touch with his feminine side.
I like to think, in a world where we've finally stopped telling children 'this is how you behave, this is what you should wear, this is what you should be playing with, this is the list of careers suitable for you,' that each child will be encouraged to try out a bit of everything and find for themselves what makes them feel happiest and most comfortable. For the majority that will mean a significant overlap between their sex, their corresponding gender identity and the things most commonly associated with that, for others it will be much less binary and that's fine.
It doesn't mean, however, that they should be encouraged to cut off their tits, wreck their fertility with hormones just so they can grow a wispy beard that fools no-one, or take their penis into women only spaces, simply by putting a skirt over it.