Dan wrote what I was thinking, pretty much. For people of my generation, doing covers is simply playing "other people's music", perhaps with an emphasis on sticking pretty closely to your favorite recorded version (an imaginative reworking of the original might be something more than "just a cover"). The intent has nothing to do with stealing sales, but with 1) playing music that the musicians enjoy, and 2) playing stuff that will go over in a club. A cover band is one that goes into bars and does just that almost exclusively. This is mostly a pop/rock usage, I would say.
Jazz standards are viewed a little differently: it's The Great American Songbook, so we're simply playing tunes "out of the book". And if we're going to play a composition by Wayne Shorter, for example, then that's how we term it: "Let's do this Wayne Shorter tune." So in organissimo's repertoire, we have our covers, our standards, and our originals.
Really, I have not put any thought into the term "cover" and no musician I've ever worked with even so much as batted an eye when it was used. It's just understood what is meant by that, and the concept of stealing sales isn't even on the radar at this level. You could accuse me/us of being historically ignorant, which I don't have a problem copping to personally, given the company here, but this is the language I inherited.