You've got my answer! Yes - I believe that the "album" the discography refers to is the generic album folder that Columbia issued between late 1943 and early 1944. As far as I know, this was not issued with discs (although that's an educated guess, based on the release information that is in the Columbia Records archive). There are no titles listed on the album front or inside the jacket. It is pictured in the 12-CD box set The Columbia Years - The Complete Recordings 1943-1952.
There is no catalog number assigned to the folio; I don't have it in front of me, so I can't verify the "C" designation. You are correct: the catalog numbers for all Columbia 10-inch, 78-RPM pop/jazz album sets contain the "C" prefix.
Hope this clarifies it...