Considerable discussion occurred in Editorial meetings in the 1970s about how to distinguish, in writing, whether a person was a native of India or an American Indian.
The words Amerindian and Asiaindian were bandied about but time and history made the decision for us.
The American Indians I have been in contact with feel that Native American is generally acceptable as meaning the many Nations and tribes which make up the Native American population of the United States.
In Hawaii there was an upsurge in the pride among the indigenous peoples of those islands in the early 1980s and Native Hawaiian, meaning a person carrying the blood of indigenous ancestors, became the acceptable phrasing.
The more you use Native American and Native Hawaiian the more trippingly it rolls off the tongue.
Odd, if I am away from the USA and people ask where I'm from I say : "Im an American, from New England," but if I am in the US I tend to say "I'm Irish American."
As an aside there's the famous (at the time) story: President Franklin D. Roosevelt, when addressing the Daughters of the American Revolution (?) began his remarks by addressing the assemblage : Fellow immigrants ..."
Which we are, aren't we?
Unless we are Native Americans?
wow