What results from differentiating the terms sex and gender?

I have noticed that many people use the two words interchangeably. Some students of science encourage distinguishing the two.

If I am understanding correctly the differentiation is this:

“Sex” refers to the biological and physiological components of a person.

“Gender” refers to the socially constructed roles, behaviours, activities, and attributes that a given society considers appropriate for one’s sex.

What kind of impact does making such a distinction have?

I am not looking for any particular answers here and I am being vague on purpose. I am simply hoping for full discussion. If you see an angle run with it. If you see something to add to the question, knock yourself out.