For America (and in extension the american continent) it is quite clear who is ethnically native, actually it is probably one of the clearest examples there is partly because it is near in history. And already it gets messy when you dig deeper because of limited record keeping etc.
Broadly in the Americas anyone that was there before Columbus is considered native. Anyone that came after is considered migrant. Anyone born into native heritage can be considered descendant of native and thus native themselves.
British ethnicity is a thing though
British ethnicity is messy and quite complex, are we talking before or after migration of the vikings? Before or after roman rein? Are we considering Ireland or Scotland separate? What about intermixing with neighboring countries through trade? Before, in or after British colonial empire?