I've done a bit of this for TV/film stuff, and yeah there's basically two copyrights on a piece of music - there's the rights to the song in general, and the performance rights. That's why you've got to be careful with public domain recordings and check the date of the performance - if you use a song that's old enough to be public domain but a more recent recording of it that isn't, you can be in trouble.
I'm pretty sure that's also why so many trailers have weird covers of famous songs on them (usually a woman doing a slow acoustic version of a rock song for some reason) - that way they can pay for the song rights, and get some aspiring singer to record it for next to nothing so they don't have to also pay the performance rights for it.