well woman is a cultural, behavioral, psychological, identity type concept, and sex (biosex) is a biological, physical, hormonal, chromosomal, anatomical concept
How could they be "the same"
I'm not saying they don't correlate or often "match up" but that's the difference
biosex is a multicomponent characteristic, in reality there are numerous characteristics that make it up. Those include hormonal ratios, sexually dichotomous brain structures, anatomical differences (genital or Gonadal) chromosomal makeup, secondary sex characteristics. All of the can align in cis folks, or they might not be "in alignment" with folks like Intersex people, or they might change later such as with trans people
it doesn't matter much to me what indiviudals **believe**, and that's what it is, a belief. What I do know, is that medical, psychological, and social sciences are advancing and updating their understandings of sex, and I can tell you, our fantastically oversimplifying of sex into a binary is inherently not accurate
Beyond that, gender is a while different ballpark.