First thing you have to understand is that DC operates in a Multiverse.
Supergirl is Kara Zor-El from Earth 0, the main Earth.
Power Girl is Kara Zor-El from Earth 2.
The difference between the two is that E-2 is where all the Golden Age stories are supposed to have happened.
Instead of Barry Allen you have Jay Garrick as the Flash, instead of Hal Jordan and the GL Corps, you have Alan Scott as the only Green Lantern.
Batman settled down with Catwoman and had a daughter Helena. Superman married Lois sooner and raised Kara, who came to earth sooner.
