cowboy hat vs hat

cowboy hat and hat both are nouns.

Word	Noun	Adjective	Verb	Adverb
cowboy hat	Yes	No	No	No
hat	Yes	No	Yes	No

As nouns, hat is a hypernym of cowboy hat; that is, hat is a word with a broader meaning than cowboy hat:

cowboy hat: a hat with a wide brim and a soft crown; worn by American ranch hands
hat: headdress that protects the head from bad weather; has shaped crown and usually a brim

Other hypernyms of cowboy hat include chapeau, lid.

cowboy hat (noun)	hat (noun)
a hat with a wide brim and a soft crown; worn by American ranch hands	an informal term for a person's role
	headdress that protects the head from bad weather; has shaped crown and usually a brim

cowboy hat (verb)	hat (verb)
	put on or wear a hat
	furnish with a hat