ice chest vs cooler

ice chest and cooler both are nouns.

Word	Noun	Adjective	Verb	Adverb
ice chest	Yes	No	No	No
cooler	Yes	No	No	No

As nouns, ice chest and cooler are synonyms defined as:

ice chest (noun)	cooler (noun)
a refrigerator for cooling liquids	a refrigerator for cooling liquids
	a cell for violent prisoners
	an iced drink especially white wine and fruit juice