mute swan vs swan

mute swan and swan both are nouns.

Word	Noun	Adjective	Verb	Adverb
mute swan	Yes	No	No	No
swan	Yes	No	Yes	No

As nouns, swan is a hypernym of mute swan; that is, swan is a word with a broader meaning than mute swan:

mute swan: soundless Eurasian swan; commonly domesticated
swan: stately heavy-bodied aquatic bird with very long neck and usually white plumage as adult

mute swan (noun)	swan (noun)
soundless Eurasian swan; commonly domesticated	stately heavy-bodied aquatic bird with very long neck and usually white plumage as adult

mute swan (verb)	swan (verb)
	to declare or affirm solemnly and formally as true
	move about aimlessly or without any destination, often in search of food or employment
	sweep majestically