Pink performed "Whataya Want From Me" yesterday at her concert in Germany. The song was written by her and recorded but not released, and Adam Lambert went on to record it for his debut album and turned it into a hit.
While intro'ing it, she said, "So I wrote this really silly song, and then I found a guy that could sing it way better than me, so it became his, and now I'm gonna sing it."
Here's video of her performance, from GolluM1973:
I don't know how to classify this. Is it a cover if it's her own song? Or is it a cover of a cover? Ehh, whatever it is, it's pretty cool that she sang it. Obviously she wouldn't be doing it if Adam hadn't made it popular, so good on both of them.