There are those that do not want to present as woman but feel feminine and dress to satisfy how they feel. It is a personal thing and there is nothing really defined but loose ground rules. This is how I see it.
To me if you identify yourself as a woman you are stating a fact that you are, ergo, a woman. The next is presenting as a woman. It would seem a blurred definition between the two statements but if you were transgender the two are separate issues. As a crossdresser you may not identify but want to present as one. A trans person may want to fully transition to make the presentation as female as they can.
Living as a woman for a transgender person is the natural goal to encompass all three statements. As a crossdresser it can be the goal but the presenting more important. Living as a woman in both cases is pretty much the same. Presenting as a woman is key as is taking up the mannerisms expected and hiding any masculine traits. Living could involve things such as work, maintaining a home and even a relationship but taking the feminine aspect.
I have to disagree with those that say you cannot transition without HRT or surgery. Here in the U.K. the health service definition states that can be all or part and even none. It is the psychology that matters. It’s the outcome the person wants to live the life as a woman because, taking your three parts a person has taken at least the last two, presented and is living as a woman. They have taken on the role as a woman by a transition.