cowboy hat vs ten-gallon hat

cowboy hat and ten-gallon hat both are nouns.

Word	Noun	Adjective	Verb	Adverb
cowboy hat	Yes	No	No	No
ten-gallon hat	Yes	No	No	No

As nouns, cowboy hat and ten-gallon hat are synonyms defined as:

cowboy hat and ten-gallon hat: a hat with a wide brim and a soft crown; worn by American ranch hands

cowboy hat (noun)	ten-gallon hat (noun)
a hat with a wide brim and a soft crown; worn by American ranch hands	a hat with a wide brim and a soft crown; worn by American ranch hands