social dancing vs terpsichore

social dancing and terpsichore both are nouns.

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

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

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

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

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