ritual dance vs dancing

ritual dance and dancing both are nouns.

Word	Noun	Adjective	Verb	Adverb
ritual dance	Yes	No	No	No
dancing	Yes	No	No	No

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

ritual dance: a dance that is part of a religious ritual
dancing: taking a series of rhythmical steps (and movements) in time to music

Other hypernyms of ritual dance include dance, saltation, terpsichore.

ritual dance (noun)	dancing (noun)
a dance that is part of a religious ritual	taking a series of rhythmical steps (and movements) in time to music