A horse is sometimes an animal you ride, a wooden toy, a game of basketball, or a punch in the knee. They’re all horses, though.
In sociology, gender studies, cultural studies, psychology, etc, gender is a socially constructed and institutionalized concept relating to roles, attitudes, manners of dress, activities, appearances, and appropriate reactions and concerns. To say that there aren’t cultural differences in approaches to gender is kind of ridiculous. A “feminine woman” in one culture might be very different from a “feminine woman” in another. Similarly, what an American thinks of as a “man’s man” isn’t going to be reflected everywhere. In that sense, there are cultural expectations which affect the way a person views his/her role as a man/woman. Denying that there are any cultural contributions is really an untenable view. IMO, just as untenable as saying that gender is 100% socially constructed. Some things come from God, some from our family, and some from the culture that we grow up in.
As a concept, gender is differentiated from sex, which is related only to sex organs.
Of course, 99% of people use gender to mean sex, because people don’t want to say “sex” in public.