ENDONYM – name the people call themselves
Sometimes transliterated/corrupted
Othaakiiwaki → French Sac → English Sauk
EXONYM – name given by outsiders
Sometimes taken from a neighboring Native group
Lakota (“friend” or “ally”) → called by the Ojibwe “Nadowessiwag” (“little snakes”) → French Nadouessioux → English Sioux
Sometimes simply given a name by the English
Lenape (“original or real people”) → lived near the Delaware River → Delaware Indians
When in doubt — Wikipedia usually lists the most common names/spellings
COLLECTIVE NAMES FOR THE PEOPLE WHOSE ANCESTORS LIVED IN NORTH AMERICA THE LONGEST
Indians – since 1492
“Red Indians” – mostly British
"American Indians" – used in United States
Native Americans – since 1960s
Earlier usage (19th c.)=white people born in U.S.A. (not immigrants)
Both "American Indian" and "Native American" are widely used and there does not seem to be a consensus over which is preferred. It may be useful to search both terms.
Amerindians / Amerinds – since 1902
mostly used in anthropology
Aboriginals – not common in U.S.A. but seen occasionally in 19th c. and before
Indigenous people – since 1980s, more widely used since 2002, still more common in academic writing