In English, "gender" used to describe words in gendered languages. In the middle of the 20th century, Americans were too prudish to continue using the word "sex" on documents and it was replaced with "gender" as a euphemism. That led to the two words becoming more or less interchangeable. Then academics started using "gender" to refer to something like the experience of being male or female, while "sex" referred to the physical characteristics.

Some people have put it like "Gender is software and sex is hardware" or "Gender is men and women. Sex is male and female."

In that framework, someone with gender dysphoria might be considered the opposite gender from their sex; i.e. transgender.