What Style and Usage Guides Say
American Indian versus Native American
While many textbook publishers play it safe and use only Native American, the majority of style and usage guides state that American Indian and Native American are synonymous.
"The terms 'Native American' and 'American Indian' should be used in U.S. mainstream newspaper stories. Use of 'Indian' alone generally is discouraged. However, it may be used in quotes, and also in terms such as 'urban Indian.' 'Native' alone has come into common usage. It is unacceptable to use 'native American' with a lower case 'n' in native. Native peoples must be allowed to define their own names in the same way other racial or ethnic groups have defined their names. But the only truly accurate terms are specific names of tribal nations, whether they are names of the 560 federally recognized ones, the many other tribes seeking recognition from the U.S. government or the multitude of tribes throughout the other countries in the Americas."
From The News Watch Style Guide (http://newswatch.sfsu.edu/)
"American Indian/Native American: The two terms are synonymous. Some indigenous people in the U.S. prefer 'American Indian' to 'Native American.' It's best to use individual preference, if known. When possible, use national affiliation rather than the generic 'American Indian' or 'Native American,' for example, Navajo, Hopi, Cherokee. To specify someone was born in the U.S., but isn't Native American, use native-born."
From Association of American University Presses, in Guidelines for Bias-Free Writing
"American Indian: This term is favored by some over Native American, which is also accepted. Whenever possible, writers are encouraged to use the name of the specific people, e.g., Cherokee or Crow, rather than this umbrella term."
From American Psychological Association (APA), in Publication Manual of the American Psychological Association
"American Indian and Native American are both accepted terms for referring to indigenous peoples of North America, although Native American is a broader designation because the U.S. government includes Hawaiians and Samoans in this category . . . Authors are encouraged to name the participants’ specific groups."