When people speak of the Retina IIc and IIIc, they usually specify whether it's the "small c" or "big C."
The Retina IIC (Big C") is an incremental improvement over the IIc (small c).
Visually, you will notice that the viewfinder and rangefinder windows are larger and of equal size. The top deck of the IIC also is flat across, whereas the earlier IIc was stepped.
The viewfinder is much brighter in the Big C, and it is easier to focus. It also contains parallax-compensating framelines for the 35mm, 50mm and 85mm lenses, which eliminated the need for the auxiliary viewfinder. You still have to shift the focus using the scale on the underside of the lens.
The IIC, like its predecessor IIc, used the excellent coated 50mm f/2.8 Schneider-Kreuznach Xenon lens in a Synchro-Compur shutter. It's a sturdy reliable camera and takes excellent photos.
Mechanically, it's more or less identical to the IIc with the primary difference being a brighter viewfinder that has framelines for the interchangeable front elements.