water hen vs mud hen

water hen and mud hen both are nouns.

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

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

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

water 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