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...but there are TWO genders.

There are 3 genders: masculine, feminine and neuter. They exist in languages. In English they exist in pronouns and words adopted from foreign languages.

There are two sexes: male and female.

Words have meaning.

All aspergers… ahem, aspersions aside, I gotcher gender right here, buddy:

gender1
—noun

Grammar.
-(in many languages) a set of classes that together include all nouns, membership in a particular class being shown by the form of the noun itself or by the form or choice of words that modify, replace, or otherwise refer to the noun, as, in English, the choice of he to replace the man, of she to replace the woman, of it to replace the table, of it or she to replace the ship. The number of genders in different languages varies from 2 to more than 20; often the classification correlates in part with sex or animateness. The most familiar sets of genders are of three classes (as masculine, feminine, and neuter in Latin and German) or of two (as common and neuter in Dutch, or masculine and feminine in French and Spanish).
-one class of such a set.
such classes or sets collectively or in general.
membership of a word or grammatical form, or an inflectional form showing membership, in such a class.
-sex: the feminine gender.
-Archaic. kind, sort, or class.

There are 3 genders: masculine, feminine and neuter. They exist in languages. In English they exist in pronouns and words adopted from foreign languages.

There are two sexes: male and female.

Depends on the language. Some don't include neuter and everything is masculine or feminine. Or even have zero genders (really one). Some have more than three and include pluralities as a gender, or other categories. There's one well-known Australian language (if you've ever looked into this topic) that classes one gender as "women, fire, dangerous things".

Side note, Swedish is an interesting one where the unknown is defaulted to feminine, whereas in most languages, the default is masculine.