Language, for the lose... FWIW, I view myself as a woman, but if it matters, and sometimes it does, I'm a trans woman. I'm comfortable if people want to view that as something a bit distinct form "woman", up to the point they start to try to push me into male gender segregated spaces. I'm comfortable being trans. I do not view myself as less than cis women. My history is simply different, and I have a different perspective.
More is made of these labels than really needs to be. They are useful (sometimes) to communicate something general about yourself to others. For example, I generally tell people I'm transgender at some point. I do this, pretty early, because if they react badly, I know to not expend any emotional energy on them, and move on. Plenty of people don't care. A few, I think, are envious. This is insane of course, but in their minds we are the cool kids right now. Go figure!