Here's something that has always confused me: What is the difference between Power Girl and Supergirl? They both seem to be named Kara, both seem to be Superman's cousin, and both are from Krypton. Supergirl seems to be younger and less respected and better behaved; Power Girl is older and more powerful and has a sluttier costume. That's about the only difference I am aware of, having only an imperfect understanding of DC canon.
Watching Smallville, their Kara seems to have Power Girl's back story but Supergirl's last name (Zor-El). Not that the creators of Smallville care very much about the canon of the DC Universe (and neither do I), but I get the sense the creators of the DC Universe don't know, or care, much about canon either.
In researching the difference between the two heroines, I realized that I'm not the only one with this confusion, and it all, apparently, boils down to the so-called Crisis on Infinite Earths, when the DC editors decided their canon was a mess, that nothing made sense anymore, so they released all these "reality waves" that changed a bunch of parallel universes into one. Or something like that.
Of all the explanations I read, this is the one that made the most sense to me. And it barely makes sense. But it is the best I'm going to get. Essentially, it seems they are the same person, but from different realities.
So, if you're like me, and these sorts of questions keep you awake at night, now you know the answer.