CharlieSierra asked "what is a woman"...
First, I subscribe to the very pragmatic definition that "gender" is a social fact, outside of one's own thoughts. It is what OTHER people experience as to your sex. If one is perceived by others as female, one is a woman.
CS also asked what are we to do with a recognition of the difference between the two... on the medical arena:
sillyolme.wordpress.com/2014/07/09/one-size-fits-all/
But if you mean general society? First, support for the wives and girlfriends of autogynephilies:
sillyolme.wordpress.com/advice-for-wivesgirlfriends-of-autogynephiles/
Ensure that such women are NOT required to pretend that their experiences don't matter... and that they have to pretend that "of course dear... you were always a delicate, sweet, feminine, little girl... and I should have taken better care to not expect you to be the man of the house..." Ensure that such women know that these transgender folk are NOT like me!
Third, and perhaps unless you actually live in a community with a high number of such AGP transwomen, this won't apply... but I and others like me have experienced this because we are out numbered by at least 4 to 1... where I have to fight misconceptions that this conflation of the two types causes in even our personal lives:
"No, it is NOT my weekend to be with my daughter! No, I've never met her bio-mom. No, I have never had sexual intercourse with a woman. I adopted my daughter... and my HUSBAND is her adopted father!"
To a bisexual woman who was informed (against my wishes) of my history, "No, I'm not interested in having sex with you... I don't care if you have had sex with other transwomen... I'm not interested."
At a political gathering of transfolk and their wives, when talking to some of the women gathered away from their 'spouses'/'husbands': "No, my husband is NOT transgendered... I'm transsexual", met with incredulous stare since this wife thought she could "read" transwomen... and she was right, if limited to only AGPs:
sillyolme.wordpress.com/2015/12/13/a-passing-moment/