marsh hen vs mud hen

marsh hen and mud hen both are nouns.

Word	Noun	Adjective	Verb	Adverb
marsh hen	Yes	No	No	No
mud hen	Yes	No	No	No

As nouns, marsh hen and mud hen are synonyms defined as:

Other synonyms of marsh hen include American coot, Fulica americana, water hen.

marsh hen (noun)	mud hen (noun)
any of various small aquatic birds of the genus Gallinula distinguished from rails by a frontal shield and a resemblance to domestic hens	a coot found in North America
a coot found in North America