I remember some years ago when I first heard the term "trans woman", I thought it meant female-to-male, rather than male-to-female or, not even that, but male-identifying-as-female (without necessarily any meaningful transition as traditionally understood).
It was a clever move in itself (on the part of the TRA movement) to choose the term "trans woman" because it sounds as though it designates a subset of women, and therefore makes "TWAW" sound tautological rather than controversial / up for debate.