wild rice vs food grain

wild rice and food grain both are nouns.

Word	Noun	Adjective	Verb	Adverb
wild rice	Yes	No	No	No
food grain	Yes	No	No	No

As nouns, food grain is a hypernym of wild rice; that is, food grain is a word with a broader meaning than wild rice:

Other hypernyms of wild rice include cereal, grain.

wild rice (noun)	food grain (noun)
grains of aquatic grass of North America	foodstuff prepared from the starchy grains of cereal grasses
perennial aquatic grass of North America bearing grain used for food