There is an ambiguity in words. If someone says "American" does one include everyone from the continents of North and South America. Does "Indian" include the whole Indian subcontinent, or only the modern state of India.
"Indian" is used for Native Americans, and people from (or descended from) India or the Indian subcontinent. This is played for laughs in The Simpsons
Apu: I am no longer an Indian living in America; I am an Indian American.
Lisa: You know what, Apu, in a way, all Americans are immigrants; except Native Americans.
Homer: Yeah, native Americans like us.
Lisa: No I mean American Indians.
It is normally not necessary to talk about someone's race. On those rare occasions when it does become necessary you should use terms like "Native American", or "First Nation" in Canada. If someone uses the term "Indian", it is probably clear from context which meaning is meant, or it doesn't matter.
Give this paper to Kat
She's the Indian woman in the end cubical.
There is an ambiguity, but it doesn't matter. In fact the last speaker should have just said "She's in the last end cubical", as it wasn't necessary to mention Kat's ethnicity.
There may be very rare situations in which precision is needed. In which case you can ask for clarification. But note the warnings: It is normally not necessary to discuss someone's race, and the ambiguity, if it arises, often doesn't matter.