flat cap vs cloth cap

flat cap and cloth cap both are nouns.

Word	Noun	Adjective	Verb	Adverb
flat cap	Yes	No	No	No
cloth cap	Yes	No	No	No

As nouns, flat cap and cloth cap are synonyms defined as:

flat cap (noun)	cloth cap (noun)
a flat woolen cap with a stiff peak	a flat woolen cap with a stiff peak