KMT: The Republic of China (ROC) is a sovereign nation-state that exercises de jure constitutional sovereignty over all areas under PRC control, Taiwan, Penghu, Matsu and Kinmen but which only exercises de facto constitutional and military sovereignty over Taiwan, Penghu, Matsu and Kinmen. Taiwan does not exercise sovereignty because it is a 'region' of the Republic of China.
Note: Taiwan and Penghu are not explicitly mentioned as territories of the ROC in the 1946 ROC Constitution (instead, it makes reference to the previous short-lived 1936 Constitution. Neither the 1923 nor 1912 ROC constitutions made reference to Taiwan, the latter explicitly naming the geographical areas covered. It was in the mid-1930's that Taiwan and Penghu got appropriated by both the CCP and KMT to be included in the constitution despite these being Japanese territories at the time).
DPP: The Republic of China on Taiwan is a de facto sovereign independent nation-state. Taiwanese exercise political and military sovereignty, generated, legitimised and sustained by its democracy, over Taiwan, Penghu, Matsu and Kinmen but under the formal name of the Republic of China (Taiwan). The two titles 'Taiwan' and 'ROC' are mutually equivalent in meaning and interchangeable. The Republic of China currently exercises sovereignty on behalf of Taiwanese pending the ability for Taiwan to complete its democratic transition from ROC constitutional republic to a de jure nation-state under the constitutional name of Taiwan.
Note: An overwhelming majority of Taiwanese citizens may regard themselves culturally as Chinese but equally overwhelmingly also regard themselves as collectively exercising a Taiwanese rather than Chinese nationality which constitutes an active, shared and vibrant Taiwan nation-hood. Given a clear choice, and without concern for the preference or cognitive bias of the audience, more than 80% of citizens on Taiwan identify themselves as politically Taiwanese. ...
