The difference is knowing that gender is a set of socially imposed stereotypes, or believing that your preferences are as a result of your sex. And if they go against your sex you must be the other sex.
It makes me laugh, and despair in turn.
Cooking for a family seems to be a female stereotype, being a famous chef, not so much.
Sewing, making curtains etc, a female stereotype. A tailor on Savile Row, not so much.
Being interested in fashion, handbags, shoes and how to make clothes look good is a female stereotype. A famous fashion designer, not so much.
Being emotional and over excited, a female stereotype. Jumping up and down screeching in glee or despair at a football match, not so much.
Most of these 'masculine' or 'feminine' behaviours are utterly imposed, and twisted or interpreted, depending upon which sex you're imposing them on.
I have no doubt that a man who sees these 'women' behaviours and wants them, feels as though his sex won't allow him to have them.
The difference is he thinks he needs to change sex to get them, whereas feminists think he should be able to have them irrespective of his sex. And vice versa for women.
Also, if gender identity is innate, how do you account for gender fluidity?
I know the reason, but having a zillion different genders to label and categorise normal human behaviour is another way that sex based oppression is ignored and sidelined.