That actually confused a lot of people (and still does, although it's not as relevant today). I would look at an actually issue of ALL-STAR COMICS from 1944 and an issue of JUSTICE LEAGUE from 1964. The Doctor Fate in each comic was not really the same, one was Golden Age and one was Earth-Two. And the Earth-Two characters would be tweaked and revised as time went on, but the Golden Age guys were frozen in the actual comics published so long ago.
The Earth-Two Superman really is not to be found in actual Golden Age comics you can collect and hold in your hand. He was a modern construct incorporating elements from the Golden Age character but he was not the same.
This actually caused some lengthy over-emotional debates and skirmishes back then, but such are the ways of fandom.