No, you just have a misunderstanding of the definition of gender and sex in terms of biology. The biological sex of an organism, where it matters, is based on chromosomes and DNA distribution. Gender is a societal-performative role that is ascribed to a person based on a number of factors. While most recorded historical societies had gender closely follow biological sex and procreative ability, there are recorded societies that followed a non-binary gender system.

The confusion between gender and sex can be understandable to those whose experience has never ventured outside of the normal of the majority. It's a specific thing but they're different words for a very specific reason and the two aren't synonyms as well for the same reasons.

Sexuality is also a separate thing from gender and sex as well. Sexuality can define different characteristics based on the organism being referred to, but it pertains to how an organism behaves in expressing it's desire find a mate and have sex, the act. Possibly leading to procreation or for the satisfaction of the participant organisms, it doesn't matter since sexuality is about the journey and what it wants to bring with it. Sexuality is a murky pool that can't really be stratified and is a big topic to be discussed.