The artwork for a song from an album makes sense to be the same--as it's a song from the album. The application won't necessarily know (And the user not necessarily care) that the rest of the songs exist or not.
As for singles, historically, they always got their own artwork. I'm not sure if they still do. I know some music services do release separate 'singles' releases and do have their own artwork, but a lot of 'singles' that get airplay are often not released as individual digital singles.
The other catch is that even though a song may be released as a single, it often would be the exact same song also found on the album. So, from a digital management standpoint, it's still the same thing.
So some things to consider.
Ultimately, in a digital world, the only differentiation between a single and a song from an album would be a bit of meta data. The obvious one would be artwork. Ideally, there'd be a meta field to signify a 'single' version of a song, but that would still be tricky when the single is the same version as from the album.
I think it may come down to two things:
- how do you separate the concept between a single and a song-from-and-album? To figure that out, you may need to do some use-case experimenting. How and why would a user differentiate between the two?
- Once that's figured out, I believe you want to come up with an icon based solution. If it's a song-from-an-album, show the album artwork. If it's a song-from-an-album released as a single, show the album artwork with a 'this is a single' icon identifier overlaying it.