Gender is different though. Because it has no definition.
'Gender identity' are the two words that are always used.
You are identifying with a different gender. An inner sense. But gender itself can't be defined.
The question asked is, when you say your gender, what do you mean? When you have that inner monologue with yourself and you identify the thing that you think you are, what is that thing.
So, say the answer is 'a woman'.
What, exactly, is it about a woman that you think you are?
There is no answer. There can't be. Because a woman is not a walking set of stereotypes. The only thing that makes a woman different to a man is her genitalia/biology. A man can't identify with a woman's genitalia/biology. He can't say that is what I am.
He can't say I am a male person with a female set of genitals.
So saying gender is an inner sense of something, completely falls apart when you asked what that inner sense is.
Except that is exactly What transwomen do say.
I am a man with a female set of genitals that look exactly like, and function in exactly the same way, as a man's does.
And not only have people accepted this, they are creating laws around it.
And guess what, the word gender is never defined in those laws. Only gender identity.