swan vs mute swan

swan and mute swan both are nouns.

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

As nouns, mute swan is a hyponym of swan; that is, mute swan is a word with a more specific, narrower meaning than swan:

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

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

swan (verb)	mute 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