'C' is generally used when it is the name of a formal party (like the Communist Party of France) and 'c' is used when one is discussing the communist socio-economic system or ideas in general.
It's hardly a rule that one has to stick to. 
personaly, I don't care whether 'C' or 'c' is used in any situation, and I use either randomly. Some people use the capital as a sign of 
respect, but that's kind of silly. 'C' or 'c' doesn't mean any ideological difference.
	Quote:
	
	
		| I'm hoping that will suffice as your sentence, Zhukov... | 
	
 Oh, You shouldn't have.
	Quote:
	
	
		| I'm sure most of us are quite aware of communist theory. | 
	
 I'm impressed.
By the way, the Stalin sig is a Vince quote, I'm not a stalinist if anyone cares.