home fries vs white potato

home fries and white potato both are nouns.

Word	Noun	Adjective	Verb	Adverb
home fries	Yes	No	No	No
white potato	Yes	No	No	No

As nouns, white potato is a hypernym of home fries; that is, white potato is a word with a broader meaning than home fries:

home fries: sliced pieces of potato fried in a pan until brown and crisp
white potato: an edible tuber native to South America; a staple food of Ireland

Other hypernyms of home fries include Irish potato, murphy, potato, spud, tater.

home fries (noun)	white potato (noun)
sliced pieces of potato fried in a pan until brown and crisp	an edible tuber native to South America; a staple food of Ireland
	annual native to South America having underground stolons bearing edible starchy tubers; widely cultivated as a garden vegetable; vines are poisonous