mud hen vs water hen

mud hen and water hen both are nouns.

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

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

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

mud hen (noun)	water 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