icebox vs cooler

icebox and cooler both are nouns.

Word	Noun	Adjective	Verb	Adverb
icebox	Yes	No	No	No
cooler	Yes	No	No	No

As nouns, cooler is a hyponym of icebox; that is, cooler is a word with a more specific, narrower meaning than icebox:

Other hyponyms of icebox include ice chest, electric refrigerator, fridge.

icebox (noun)	cooler (noun)
white goods in which food can be stored at low temperatures	a refrigerator for cooling liquids
	a cell for violent prisoners
	an iced drink especially white wine and fruit juice