Indiano vs. índio
While English often uses Indian for two very different groups, Portuguese makes a strict geographical distinction. Use indiano for the Asian country and índio for Indigenous peoples of the Americas. Using índio to refer to someone from India is considered incorrect in modern Portuguese.
Indiano
A2This adjective and noun refers strictly to the country of India in Asia. You should use indiano when discussing the nationality, culture, religion, or cuisine of the Indian subcontinent.
Eu adoro comer comida indiana nos fins de semana.
(I love eating Indian food on the weekends.)
O governo indiano investiu muito em tecnologia.
(The Indian government invested heavily in technology.)
Ela se casou com um rapaz indiano que conheceu em Nova Delhi.
(She married an Indian guy she met in New Delhi.)
A música clássica indiana é muito complexa.
(Indian classical music is very complex.)
Índio
B1This word refers to the Indigenous peoples of the Americas (Native Americans/First Nations). Historic confusion arose because explorers thought they reached the Indies, but in modern Portuguese, índio never means a person from the country of India.
Os índios habitavam o Brasil muito antes da chegada dos europeus.
(Indigenous people inhabited Brazil long before the arrival of Europeans.)
Ele estuda a cultura do índio brasileiro na universidade.
(He studies the culture of the Brazilian indigenous person at the university.)
A preservação das terras dos índios é fundamental.
(The preservation of the lands of the indigenous people is fundamental.)
Muitos índios falam línguas nativas além do português.
(Many indigenous people speak native languages in addition to Portuguese.)
Summary
To avoid confusion, remember: if the subject is related to Asia (Taj Mahal, curry, Hinduism), use indiano. If the subject is related to the native inhabitants of the Americas (Amazon tribes, pre-colonial history), use índio.