duet vs dancing

duet and dancing both are nouns.

Word	Noun	Adjective	Verb	Adverb
duet	Yes	No	No	No
dancing	Yes	No	No	No

As nouns, dancing is a hypernym of duet; that is, dancing is a word with a broader meaning than duet:

duet: (ballet) a dance for two people (usually a ballerina and a danseur noble)
dancing: taking a series of rhythmical steps (and movements) in time to music

Other hypernyms of duet include dance, saltation, terpsichore.

duet (noun)	dancing (noun)
(ballet) a dance for two people (usually a ballerina and a danseur noble)	taking a series of rhythmical steps (and movements) in time to music
a musical composition for two performers
a pair who associate with one another
two performers or singers who perform together
two items of the same kind