Names for Indigenous Peoples

Names for Indigenous People in The Americas
Names for Indigenous People in The Pacific

Why do we use "Native American" for indigenous people in the United States, but use "indio" [Indian] in Brazil and Mexico?
Why do we use "First Nation" for indigenous people in Canada instead of "Native American" ?

Where can I find more information on Native Names?

We use "Indian" in Spanish and Portuguese America BECAUSE
Spain and Portugal referred to the Americas and Pacific as The Indies. Therefore the inhabitants of these regions were properly called "Indians" just as the people who inhabit the Americas are called "Americans."
Early Spanish and Portuguese settlers referred to indigenous people derogatorily as "gentiles," or heathens outside the Christian community. Therefore aboriginal people do not consider "Indian" an insult in Spanish or Portuguese any more than Americans consider their name an insult.

We use "First Nations" in Canada BECAUSE
English French, and Dutch settlers called original inhabitants "nations" [natie in Dutch]. In the nineteenth century, French-, English-, and Dutch speakers began to insist their states were nations and used the ancient Latin term "tribes," for those "nations" whose political organization they considered unsophisticated. Thus the New World's original inhabitants became "tribes' instead of "nations." Twentieth-century indigenous communities in Canada have insisted upon their political equality and invoke their prior occupation of the continent by referring to themselves the "First Nations."

Why we use "Native Americans" in the United States:
In the United States, however, indigenous peoples have preferred to be called Native Americans, sharing the label with most US citizens, who usually call themselves as "Americans." By choosing the adjective "native" they have chosen to highlight the difference between themselves and the "immigrant" or hyphenated Americans.

SUMMARY
Canada has First Nations

United States has Native Americans

O povo indígena do Brasil se denomina "indios."

Desde Mexico a Argentina y Chile, pueblos indígenas se llaman "indios."