wild rice vs Indian rice

wild rice and Indian rice both are nouns.

Word	Noun	Adjective	Verb	Adverb
wild rice	Yes	No	No	No
Indian rice	Yes	No	No	No

As nouns, wild rice and Indian rice are synonyms defined as:

wild rice (noun)	Indian rice (noun)
grains of aquatic grass of North America	grains of aquatic grass of North America
perennial aquatic grass of North America bearing grain used for food