Pieces of paper vs papers

Yes, although it would be ambiguous. "Papers" almost always refers to documents--pieces of paper which have writing on them already, at the time of referring to them. It would be better not to do so, so as to avoid confusion. This is one of those questions which it is difficult to answer without context.

Thanks, Setanta.

You're welcome.

Cigarette and fly papers usually don't have anything written on them.

What part of "almost always" didn't you understand?

No part of it. I wasn't disputing what you wrote.