stage dancing vs dancing

stage dancing and dancing both are nouns.

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

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

stage dancing: a show involving artistic dancing
dancing: taking a series of rhythmical steps (and movements) in time to music

Other hypernyms of stage dancing include dance, saltation, terpsichore.

stage dancing (noun)	dancing (noun)
a show involving artistic dancing	taking a series of rhythmical steps (and movements) in time to music