What does it mean to be "assigned male at birth"? You are either born male or you are not, no?
It means you were assigned based on your external genitalia rather than the gender you "really" are inside.
I put really in the scare quotes because if gender is a social construct rather a bit of physical anatomy, then no one is "really" a particular gender.
It's neither. If gender were determined by sex, trans people wouldn't exist by definition. If gender were a social construct, every tomboy would just be a boy (if, of course, I am understanding those social-construct people).