The Commodore 64C was simply the original C-64 repackaged in in a beige C-128 style case. Internally, Commodore integrated most of the hardware onto a single VLSI chip.
The new model did not differ much from its predecessor, the only innovation was the flatter case, which made the keyboard (which had off-white keys) more ergonomic (it looked like the C128 case), not as high as than the old one. But the new case did not only have advantages: due to its low profile and additional metal screening, some of the numerous hardware expansions did not fit anymore. This was changed with the C64G.
The official name for this model was "C=64 C", but nevertheless the German 64'er magazine decided to call it "C64-II" (because the first units didn't have the new name on the label at the bottom), the badges on most of the 64 C's just says "Commodore 64". They pointed out that this name was only valid for the 64'er magazine, but since the 64'er was the magazine for the C64 for a long time, the name was widely accepted and so this model is mostly known as "C64-II" in Germany.
Commodore took advantage of the launch of the 64C to improve its range of peripherals. The machine could be delivered with:
• the 1541C disk drive, internally the same as the previous 1541, but with a beige case,
• the 1541-II disk drive, a smaller 1541 with external power supply and a beige case
• The 1351 two-button mouse which could operate in either proportional or joystick mode,
• The 1802 color monitor which accepted both composite and RGB video signals,
• The 1764 RAM expander which plugged into the expansion port and boosted the system RAM to 256 KB.
First 64C were bundled with GEOS, developed by Berkeley Software, a good window and icon opating system, considering that it ran on a 8-bit processors and 64 KB of RAM.
Sadly, the 64C was launched at the wrong time, at a wrong price (about $80 more than the C64). At that time the competition was hard with the new Atari and Amiga 32-bit computers. The 64C thus didn't meet a large success, except in some European countries.