The "C" refers to the Cohen number, the variety designator that the vast majority of collectors use. It refers to Roger S. Cohen, who cataloged the known varieties of
US Half Cents starting in about 1971, and his numbering system, based on the supposed emission sequence of the varieties, is the standard used by EAC
Half Cent collectors, and the vast majority of serious copper collectors.
Prior to Cohen, there was a guy named Ebenezer Gilbert who did the same thing cataloging varieties in 1916. Walter Breen is a "Johnny-come-lately" who, although a decent numismatist, was an egomaniac of the highest level, and he just assumed that his new numbering system for practically all
US coins would be readily accepted by all collectors everywhere. He was wrong. His system is cumbersome and was never really considered for standard usage.
The reference I use for variety identification is "The
Half Cent Die State Book 1793 - 1857" by Ron Manley. It is the newest, and by far the best reference ever written on varieties and die states of
US Half Cents. It is considered to be the standard reference on the subject now. The photos are outstanding. I got my copy from Charles Davis, a numismatic and rare bookseller who is on
ebay as "numislit". You can buy them directly from Ron Manley, but I can't seem to find his contact information right now.
Hope that helps
