If you want to talk straight semantics, consider the following definition from Oxford: "Gender: Either of the two sexes (male and female), especially when considered with reference to social and cultural differences rather than biological ones. The term is also used more broadly to denote a range of identities that do not correspond to established ideas of male and female."
Sex is what they are biologically
Gender is what they feel mentally.
If I were to transform this into your Elvis equivalency.
Existence: I am not Elvis
Personality: I feel as if I am Elvis. I will be an Elvis impersonator for the rest of my life.
Even if you agree with it or not, there are thousands of examples of people who are one sex, but feel mentally as if they are another. By definition, sex and gender are two different things.
The 'more than two genders' thing, which seems to be confusing you, comes from the idea that some people don't feel either fully in the male side, or fully in the female side of gender identity. I can see why this may seem strange to most, because it's not a part of your everyday life, and people are only starting to feel comfortable exploring who they really are, gender wise. It's also more rare than people who just want to go full male identity, or full female identity. This is where the term non-binary comes from, because they don't choose the two options, they fall somewhere in the middle. The fact that some people feel this way means you have to make a scale, rather than a binary.
If you require further help, please try this image of a gingerbread man. Gender is in the brain, sex is in the genitals, and sexual orientation is what you want to fuck.
I'm not gonna get into the expression box, cause I don't know anything about that.