top hat vs high hat

top hat and high hat both are nouns.

Word	Noun	Adjective	Verb	Adverb
top hat	Yes	No	No	No
high hat	Yes	No	No	No

As nouns, top hat and high hat are synonyms defined as:

top hat and high hat: a man's hat with a tall crown; usually covered with silk or with beaver fur

Other synonyms of top hat include beaver, dress hat, opera hat, silk hat, stovepipe, topper.

top hat (noun)	high hat (noun)
a man's hat with a tall crown; usually covered with silk or with beaver fur	cymbals that are operated by a foot pedal
	a man's hat with a tall crown; usually covered with silk or with beaver fur