The Republic of China: Kuomintang (and its successors)
The People's Republic of China: CCP.
Been that way since about 1949, right?
(Or, did the folks on Taiwan one day drop the RoC appellation? I might have missed a memo)
I recall a similar distinction between East and West Germany: FDR and DDR, back in the day. (Also see the reference to Kim et al above)