CMSNL has both the '80 CB650 and the '80 CB650C carbs as the same part number. I would assume that you could use the same rebuild kits but I don't know these bikes too well.
It's a good idea to keep the brass (jets, emulsion tubes, needles and float needles) you have and clean them up with wire, carb cleaner and compressed air rather than use the brass that's in the kits. The brass that the kits come with are of lesser quality and without the tight tolerances of OEM. The rubber bits and gaskets are fine to use as long as they're fuel resistant. Besides, the brass is rarely damaged, just clogged.