social dancing vs dancing

social dancing and dancing both are nouns.

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

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

social dancing: dancing as part of a social occasion
dancing: taking a series of rhythmical steps (and movements) in time to music

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

social dancing (noun)	dancing (noun)
dancing as part of a social occasion	taking a series of rhythmical steps (and movements) in time to music