This is the everyday noun for a person from the country India. It counts: an Indian, two Indians. English writes it with a capital I, because it is built on the country name India. In ordinary talk the adjective is more common than the noun, so most speakers say she is Indian rather than she is an Indian. The same spelling also names a member of the native peoples of the Americas, who are a completely different group of people, so the place and the time in the sentence usually tell you which one is meant. In American English, a speaker who wants to keep the two apart may say Asian Indian or Indian American for this meaning.

This is the adjective built on the country name, and it sits in front of a noun or after be: Indian food, an Indian film, the Indian government, my flatmate is Indian. It is the form people reach for most when they talk about a person: she is Indian is far more common in speech than she is an Indian. Keep the capital I even in the middle of a sentence. In older writing you may meet it stretched over a much wider area — the East Indies, or anywhere east of Europe — but that use has dropped out of ordinary modern English.

The name came from a mistake. The first European sailors believed they had reached the Indies, and the word stayed on people who had no connection with India at all. Today, using the bare word Indian for this meaning is widely avoided in the United States and Canada; this use is proscribed, which means many careful speakers and editors advise against it. What people say instead: Native American, Indigenous, American Indian, First Nations in Canada, or, most precisely, the name of the person's own nation — Navajo, Cherokee, Ojibwe. You still meet the bare word constantly, because it is fixed inside older books, place names, team names and official terms such as Indian reservation and the Bureau of Indian Affairs. So a reader needs to recognise it. Recognising it and choosing it yourself are two different decisions, and the specific nation name is the safer choice when you speak.

This is the adjective that goes with the Americas meaning of the noun, and it carries the same naming history: the word came from a European mistake about where the ships had landed. The modern use is proscribed, and in most new writing the adjective of choice is Native American, Indigenous, or the specific nation — Navajo art, Hopi land. The bare adjective survives strongly inside fixed official names, where it cannot simply be swapped out: Indian reservation, Indian Country, the Indian Child Welfare Act. Those are legal terms, not casual description. So you read it often and choose it rarely.

This is a short cut: the full phrase is an Indian meal or an Indian restaurant, and speakers drop the second word. It counts, so it takes a or the, and it appears mostly in a few set frames — go for an Indian, fancy an Indian, order an Indian, there is a good Indian near here. It is British English and informal, so it belongs to friends making plans rather than to a written review. American speakers usually keep the longer wording: get Indian food, go to an Indian restaurant. British English does the same trick with other cuisines, which is why you also hear go for a Thai or grab a Chinese.