Sol and Joe Offer, I agree that "version" is a better word than "cover".
A "Cover Band" doesn't do their own version of the songs of the band they are covering. They try to sound like the band. Often they even try to look like the band.

Remember the K-Tel (sp?) days when a cover was an exact (as exact as possible) copy of a hit song, complete with every lick and even every mistake.
Musicians like Billie Holiday, Ella Fitzgerald, Joe Williams and Sarah Vaughan were not called "Cover artists", even though they sang other people's songs, because they didn't try to sound like another artist, they did their own "version".
The same is true of instrumentalists. When Charlie Parker played "Just Friends", or Thelonious Monk played "April In Paris" it wasn't called a cover.