choreography vs dancing

choreography and dancing both are nouns.

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

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

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

Other hypernyms of choreography include dance, saltation, terpsichore.

choreography (noun)	dancing (noun)
a show involving artistic dancing	taking a series of rhythmical steps (and movements) in time to music
the representation of dancing by symbols as music is represented by notes
a notation used by choreographers