baked potato vs Irish potato

baked potato and Irish potato both are nouns.

Word	Noun	Adjective	Verb	Adverb
baked potato	Yes	No	No	No
Irish potato	Yes	No	No	No

As nouns, Irish potato is a hypernym of baked potato; that is, Irish potato is a word with a broader meaning than baked potato:

baked potato: potato that has been cooked by baking it in an oven
Irish potato: an edible tuber native to South America; a staple food of Ireland

Other hypernyms of baked potato include murphy, potato, spud, tater, white potato.

baked potato (noun)	Irish potato (noun)
potato that has been cooked by baking it in an oven	an edible tuber native to South America; a staple food of Ireland