Adding to what you said, I feel like people use a wrong term when addressing their sexual orientation. Sex of a person simply refers to their physical characteristics that they're born with, therefore, the person can either be a male or a female. Again, when the person gains a good enough consciousness to decide for themselves what they prefer sexually/emotionally, that can be called their gender (straight, gay, lesbian, bi, etc).

So, there can only be three sexes, 2 are those with which people are born with, and one is transgender where they can change their sex as per their preference. On the other hand, genders can be unlimited as there is no end to what people like in particular.

It is nothing more than a simple definition mix-up for most of the individuals :)