As I understand it, there's a mandatory licensing scheme for releasing cover versions.
Say for example that I decide to record my own version of Imagine by John Lennon with the same melody and lyrics and release that on CD. No one can stop me from doing that, but for every copy sold, I have to pay whoever owns the author rights a certain amount. I'm sure there's a complicated formula for determining that amount.
I could also decide to release Imagine with my own changes to the melody and lyrics. It's still obviously Imagine by John Lennon but with my own special touches. Same deal there. I release it commercially and send Yoko Ono an amount determined by a formula.
Another possibility is I do a Weird Al type song. The melody is obviously Imagine, but with entirely new lyrics about how good waffles are. I release that commercially, but now I only have to pay for the use of the melody since I used my own lyrics.
That's all for releasing just a cover version of a song. Performing that at a live event means the venue has to pay BMI or ASCAP a fee for public performances. Broadcasting it on TV as a performance is another thing. I believe using it in an advertisement is an entirely separate thing and not mandatory. When it comes to advertising, the original author gets the right to say they don't want their work to be used to endorse something.
We can see examples of this when the next election season comes up in the US. Some politician will use a song at their rallies and the singer/songwriter will make a big deal about how they think that politician is a moron, but it's not clear if they can stop them from using it at rallies. Then some politician will use the song in a political TV ad. Charlie Crist had to apologize on Youtube as part of a settlement for using one of David Byrne's songs.