Regarding "woman" vs "adult", I think (hope) in this case they refer to the same thing since, unless I'm mistaken, we are all females here and thus obviously we're women. I -do- think the experiences we have as females differs significantly from men in many ways in part due to different biology and as well as social expectations and prejudices.
As an example, my DH and I have been together nearly 20 years. We don't have kids. Many people find that unusual and I especially take heat for it on occasion. DH never gets that. Ever. Society has expectations about what I should want and be like as a female. That certainly affects who I am. Those sorts of things affect all of us.
I'm happy to say, however, that at 40 I definitely get less guff about it. I think things have started to change too, and that choosing a life without children has become more accepted and common. Biology is not the only difference between men and woman; Sure, at birth it is. We have different parts and hormones. But gender affects life experience. Even thinking in a cold, scientific way (especially that, really) you can see how that would make a difference.
It's nature vs nurture. Both play a role in forming the individual. I come up against this all the time in my profession, and we can even make generalizations about behavioral differences based on sex, even when they are spayed or neutered.