cloth cap vs flat cap

cloth cap and flat cap both are nouns.

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

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

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