Your impressions are all true, but Taiwan hasn't given up formal claim to mainland China. This is important because it allows the "policy of deliberate ambigui

Your impressions are all true, but Taiwan hasn't given up formal claim to mainland China. This is important because it allows the "policy of deliberate ambiguity": > There is deliberate ambiguity regarding the government of the country of 'China' (as well as what land this country constitutes). Currently, two governments claim legitimate rule and sovereignty over all of China, which they claim includes Mainland China, Hong Kong, Macau and Taiwan, as well as some other islands. > those from Taiwan who attend the Olympic Games and other various international organizations and events participate under the deliberately ambiguous name of "Chinese Taipei" https://en.wikipedia.org/wiki/Policy_of_deliberate_ambiguity https://en.wikipedia.org/wiki/Policy_of_deliberate_ambiguity