Gender dysphoria is a dangerously weak term but it is inclusive of several related conditions, and could even be used to include cases where someone is happy with their body but unhappy with their gender.
For example, I felt that I was a girl for as long as I can remember but I can't say that I was dysphoric, or dysmorphic, about my body until I was eight, as until then I didn't know that boys and girls had different bodies. Even then, I am not sure that "transsexual" would have exactly described how I felt, as it was almost another two years before I had any idea about sex or how babies are really made. Even then, I didn't really have any idea, as my first clue was in a changing room when a boy, jokingly I'm sure, put his thing against my bum and said "now you'll have a baby".
When I was growing up and even as a young adult, the terminology was limited, though. In my teens and early adulthood, I learned what I could about myself from salacious newspaper stories and occasional articles in my mother's magazines. I first learned about "sex changes" and transsexuals in 1968, from the back page of a Sunday newspaper, still gossiping about April Ashley several years after she was first outed.
At least as late as my thirties, this was what I THOUGHT I knew about the subject:
"->-bleeped-<-s are people who like to wear the clothes of the opposite sex. Some ->-bleeped-<-s do it for a reason that can't be discussed on Susan's Place (I didn't know the scientific word for it then). If ->-bleeped-<-s actually want to be members of the opposite sex, they are transsexuals, unless they also want to have sex with members of their birth sex, in which case they are not transsexuals but deluded cross-dressing homosexuals." (To be fair to psychiatrists at the time, "sex change" definitely meant an end to physically enjoying sex, so surgery was not a decision to be made lightly.)
Before I turned thirteen, I knew enough to know that I am transsexual (although I fought against it like mad, as such a future seemed hopeless - SRS and even full-time transition [both terms I had never encountered] seemed unlikely). I suppose, though, that "gender dysphoria" encompasses the feelings I have had for my whole life.