bowler vs bowler hat

bowler and bowler hat both are nouns.

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

As nouns, bowler and bowler hat are synonyms defined as:

bowler and bowler hat: a felt hat that is round and hard with a narrow brim

Other synonyms of bowler include derby, derby hat, plug hat.

bowler (noun)	bowler hat (noun)
a felt hat that is round and hard with a narrow brim	a felt hat that is round and hard with a narrow brim
a player who rolls balls down an alley at pins
a cricketer who delivers the ball to the batsman in cricket