What is gender?

The way I see things, gender is a physical state of which there are three: male, female and hermaphrodite.
Whereas what a person identifies themselves to be is mind made and has no limits.
The current gender issue seems to be semantics in that gender is being seen as the mind state rather than the physical body.
If I believe myself to be a cat trapped in a human body, am I a cat with the wrong body or am I a human that thinks it is a cat?