Female and male are NOT genders: they are sexes.
people who undergo sex change operations are transexual people NOT transgender people.
Female impersonators are transgendered, or transvestites.
Gender is learned, a social creation, and specific to culture.
Race is equally arbitrary and distinguished by region and group.
Sex is about genital types. Females, males, intersex (hermaphrodite) people.
Gender can change from one day to the next in the same person. Sex is very different. It can be changed, but only after dangerous, irreversible surgical interventions.