It's not as simple as that. The word 'gender' has a history of being used for biology - think of every form you've ever filled out. The OED [1] says:
> Either of the two sexes (male and female)
before following up with:
> especially when considered with reference to social and cultural differences rather than biological ones.
And also notes:
> The sense denoting biological sex has also been used since the 14th century, but this did not become common until the mid 20th century. Although the words gender and sex are often used interchangeably, they have slightly different connotations; sex tends to refer to biological differences, while gender more often refers to cultural and social differences and sometimes encompasses a broader range of identities than the binary of male and female
If it's unclear, I'm not saying either is correct. Many people don't like saying 'sex' as its also a verb for copulation hence use 'gender' as a polite alternative. The idea of gender as an entity separate from biology is from Dr John Money, who has his own sad and controversial history [2], though his ideas have gained more popularity recently.
Webster's define (the relevant meaning of) gender, as:
"b : the behavioral, cultural, or psychological traits typically associated with one sex
(...)
Origin: Middle English gendre, from Anglo-French genre, gendre, from Latin gener-, genus birth, race, kind, gender — more at kin.
First use: 14th century"
So it would seem gender has started out as a term that groups "indivuduals that are of a kind" - not necessarily based on (biological) appearance, but just as much on behaviour/social grouping.
Language is a living thing. The meanings of words change over time, and that's normally a helpful thing, which lets us express culturally relevant concepts.
In this case, it's pretty useful to have words which distinguish between biology and culture.
If you use “ascribed gender” and “gender identity” to describe the (external and internal, respectively) social traits, you avoid the confusion between the two and with the biological trait that comes with using bare “gender” for that purpose.
> Either of the two sexes (male and female)
before following up with:
> especially when considered with reference to social and cultural differences rather than biological ones.
And also notes:
> The sense denoting biological sex has also been used since the 14th century, but this did not become common until the mid 20th century. Although the words gender and sex are often used interchangeably, they have slightly different connotations; sex tends to refer to biological differences, while gender more often refers to cultural and social differences and sometimes encompasses a broader range of identities than the binary of male and female
If it's unclear, I'm not saying either is correct. Many people don't like saying 'sex' as its also a verb for copulation hence use 'gender' as a polite alternative. The idea of gender as an entity separate from biology is from Dr John Money, who has his own sad and controversial history [2], though his ideas have gained more popularity recently.
[1] https://en.oxforddictionaries.com/definition/gender
[2] https://en.wikipedia.org/wiki/John_Money