The people's language and DNA are different, but there is evidence of contact between the two. Arcona chickens that lay green eggs were pre-Columbian, and they were originally southeast Asian Jungle Fowl before human domestication. The sweet potato of Polynesian culture is from the Americas.
Thor thought that the people went from Peru to the Pacific Islands (where the current would take you). But the language and DNA didn't back him up. But if you look at the oral history of the Pacific Islands, they claim that when they came to the island there were ‘long eared’ people, but that they, the ‘short eared’ people, killed them all.
The maori of New Zealand say the same. (And, ate them)
The American Indian said they did the same with these red-haired people: