Why can countries officially recognise both the Democratic People’s Republic of Korea and the Republic of Korea as different political entities despite them both claiming to be the true Korea, but not the People’s Republic of China and the Republic of China, instead having to choose a side?
Two reasons:
First, both Koreas accept that there are two different countries through various political actions. That equivalent doesn’t exist for the Chinas; both nations officially don’t recognize each other’s legitimacy and don’t treat each other as independent nations.
Second, the UN Veto only goes to one country. The USA kept the PRC from being declared the legitimate Chinese government. So, the world is used to viewing the issue of one China, it continues to do so.