In Greek myth, only one of the Dioscuri was the son of Zeus- the other being the offspring of Leda and Tyndareus. How was it that they BOTH became associated with the Father Zeus? Was it because 'they were lovely and together in their lives; in death they were not divided'?

I mean, was it because you couldn't basically have one without the other? To this day, I can't recall which one was god-born and which one was not without going to look it up.