I know and understand there's only one America, though in the "Americas" (which is an entirely different thing) there are many countries, across a couple of continents. Countries are easy to define, though some just barely qualify, because of the lack of functioning governments, if you ask their citizens, you'll find they consider themselves Brazilians or Trinidadians, etc., not Americans. Even in places like Somalia, where there's literally no functioning government, the citizens call themselves Somalian, not African.
Rest assured the same is true in New Zealand, where they'll quickly present a bar fight, if they're mistaken as Australians. China will have a quick, though likely short term improved relationship with the lower Pacific western rim nations, where geopolitical and natural resources can be exploited, but this is a short term goal, until their aging and dwindling workforce can be replaced by the soon to appear baby boom, that's about to occur (it is here now). With the new, fresh and young manpower force, their employment short falls will self heal and they'll return to a more centralized economic arrangement, if history is to be repeated (it always is). China is on a precipice of sorts and with the right moves can really enter the world's markets as a real player, but significant economic and geopolitical changes will be necessary to fully realize this potential, which in recent decades, it's been reluctant to perform.