mud hen vs marsh hen

mud hen and marsh hen both are nouns.

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

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

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

mud hen (noun)	marsh hen (noun)
a coot found in North America	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