they are under their own independent system of goverment with a common consensus to keep it that way creating a definite divide between the two countries, even though they share the same "blood" they should absolutely be recognized as two unique entities
yeah they are both chinese but just different "types" akin to a more extreme version of the gap between the us and canada, its the same people but due to differences in government and geography their culture spins off
Taiwan's official name in English is Republic of China and they do claim mainland China themselves, so they are definitely Chinese, at least ethnically. Disagreeing with the government of PRC politically doesn't change their genetics. It's like North and South Koreas, they are equally Korean.
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