Its not really like the US analogy. The confederates were completely beaten and surrendered. After the Chinese civil war, the CCP and Red/PLA didnt have the chops to cross the Strait to Formosa, so they just stopped, and Taiwan became its own country. Much like how North Korea and South Korea entered a stalemate and became seperate countries.

Both Taiwan and South Korea were born as dictatorships, and gradually transitioned to liberal democracy, whereas North Korea and PRC never got the memo.