I agree with them both really, but would say that for me, and if I thought I was a female trapped in the body the young boy, I didn't. I think that what really matter how you thought yourself to be was shaped by what period of time you grew up in. My quality of life was shaped by the discipline of my father. There were subjects that were never broached, or even considered. My ideas of sex and what emotional forces sex exhorted was shaped by the churches definitions and telling anyone that you wished you were a girl was a death sentence in ones social world. As a young boy living with 4 sisters, I knew what girls were like, I was having too much fun teasing them. Was the teasing out of jealousy, can't say. I know I wished on many a birthday cake and evening star to wake up like one of them.
When I was little, I have heard several of my aunties tell me that they just knew I was suppose to be a girl. That I should have been born a girl, that I was to pretty to be a boy. A boy's body I had and I grew accustomed waking up and seeing it still there. Anything feminine was mystical magical and forbidden; therefore I wanted to touch and smell and wear them.
Every step I took in my mother's heels and latter my heels that brought me ever so much closer to transition was on my own stumbling steps. Never having anyone help me or support me or meeting anyone of the lgbt community much less another person who wished they could be a girl. It wasn't until after my divorce when I was about 56 years old that I met another trans person and by that time I was well on my way to living authentically as female.
So no! I never thought myself as a girl in the body of a boy, I was a person who had a boy's body and thought that I was different. As my level of female gender acceptance grew, my female brain took over the body and adapted it to her needs and liking thus finally uniting and creating a harmonic union between the person I really was and the body she inherited.