Gender_Critical

To add a bit from one English-native-tongue perspective about "gender" and "sex":

I'm not a linguist, but I think maybe what happened in English is that "gender" became a euphemism for "sex" (as in male/female), since it's also the word for the act of sexual intercourse. It can be a little uncomfortable to say, because it sounds like you're talking about, well, having sex, when you just want to talk about whether someone is male or female. "Gender" avoids this problem.

Alternatively, maybe this difference was developed by the radfems who were developing the gender criticism discourse. I don't know whether "gender" was in common use to refer to sex or sex roles before that time. It's possible it was this discourse that helped create the separation, but I don't know. Maybe it was earlier. I don't know much about the history of the words.

Sometimes I think it's interesting where the words for these concepts come from. In English, it looks like "gender" comes through Latin, then French from "birth", and the idea of classifying things by species (like "genre"). It looks like "sex" comes through Latin from "to cut" and the idea of separating things (like "section"). Interestingly it says here that "sex" is only recorded as being used to mean "sexual intercourse" since around 1930, which seems pretty recent to me.

And it looks like etymonline agrees with what I thought about "gender":

As sex (n.) took on erotic qualities in 20c., gender came to be the usual English word for "sex of a human being," in which use it was at first regarded as colloquial or humorous. Later often in feminist writing with reference to social attributes as much as biological qualities; this sense first attested 1963. Gender-bender is from 1977, popularized from 1980, with reference to pop star David Bowie.