That claim is mutually exclusive with Taiwan being “its own nation” distinct from China. It is definitionally its own government, but it claims to be a superset of the nation of China (because of also claiming Mongolia and some smaller territories). Nations are a social construct based on historical group identities, so the PRC is the same nation as the ROC was back when the ROC controlled the mainland. The ROC claims to still be that nation (plus Mongolia) which the PRC currently administers.