The 700c comes from the French sizing convention where there were four 700 designations that ranged from A to D (narrow to wide) and although each rim was of a different size, the effective diameter of the tyre was 700mm at the outside. The 700 A, B, and D designations are now obsolete although the 650A, 650B, and 650C sizing convention is still in use.
700c is now used for any rim that is 622mm at the bead seat or any tyre that fits this rim size and the secondary number denotes casing width in mm.