"inhabit of India or South Asia; pertaining to India," c. 1300 (noun and adjective), from Late Latin indianus, from India (see India). Applied to the aboriginal native inhabitants of the Americas from at least 1553 as a noun (1610s as an adjective), reflecting Spanish and Portuguese use, on the mistaken notion that America was the eastern end of Asia (it was also used occasionally 18c.-19c. of inhabitants of the Philippines and indigenous peoples of Australia and New Zealand. The Old English adjective was Indisc, and Indish (adj.) was common in 16c.
Red Indian, to distinguish the native Americans from inhabitants of India, is first attested 1831 in British English (Carlyle) but was not commonly used in North America. More than 500 modern phrases include Indian, most of them U.S. and most impugning honesty or intelligence, such as Indian gift:
An Indian gift is a proverbial expression, signifying a present for which an equivalent return is expected. [Thomas Hutchinson, "History of Massachusetts Bay," 1765]
Hence Indian giver "one who gives a gift and then asks for it back" (1848). Indian elephant is from c. 1600; Indian corn is from 1620s; to walk Indian file is from 1758. Indian club is from 1824 as a weapon, 1825 as exercise equipment (clubs were noted noted in Lewis & Clark, etc., as characteristic weapons of native warriors in the American West). Indian-head (adj.) in reference to U.S. copper pennies with a portrait of an Indian in profile, from 1862.