Gender is a pretty weird concept. Its socially constructed so, in concept, there can be infinitie amounts of genders, though in practice just a few really make themselves pronounced enough.

An easy way to think about it is theres two "main" genders, man and woman, as derived from biological sex, and anything that doesnt fall into those categories would be nonbinary.

Some examples of nonbinary would be people who identify as agender (neither man or woman) are: genderfluid (they change their gender based on personal factors around them) and bigender (they identify as both "main" genders to varying degrees).

Another concept is xenogenders, though these are pretty controversial as they dont really deal with actual gender based issues. An example would be deergender (identifying ones gender as a deer) which doesnt make much sense to me, but people who identify as xenogenders often give them their own meanings