[ue_]

To my knowledge, gender is thought of as a complex of at least two aspects: those differences between what is thought of as masculine and feminine, and the roles assigned to genders. In these cases, gender pertains to the ideas of gender identity and further gender expression. In other cases, gender is also thought of as including or being inextricably related to biological sex.

Gender isn't "made up" in the same way that words aren't "made up"; it is an aspect of society, but unlike words, gender is with some relation to observable physical biological expression, usually termed as 'sex'. But the concept of gender as I have seen it used is certainly depending on society, rather than physical sex.

Variations within sex (such as intersex) is another question and is unrelated to gender, as far as I know.

[tomp]

The problem with "gender" as a concept is that they hijacked existing words ("man" and "woman") that were previously used for "sex". This can be clearly seen by trying to define these words without reference to sex - you can't except by defining them recursively ("men are people who identify as men"), in which case, I think a better choice would be to invent new words for this new concept.

[ue_]

Sex is to male and female as gender is to masculine and feminine.