song and dance vs performance

song and dance and performance both are nouns.

Word	Noun	Adjective	Verb	Adverb
song and dance	Yes	No	No	No
performance	Yes	No	No	No

As nouns, performance is a hypernym of song and dance; that is, performance is a word with a broader meaning than song and dance:

Other hypernyms of song and dance include public presentation.

song and dance (noun)	performance (noun)
theatrical performance combining singing and dancing	the act of performing; of doing something successfully; using knowledge as distinguished from merely possessing it
an interesting but highly implausible story; often told as an excuse	the act of presenting a play or a piece of music or other entertainment
	any recognized accomplishment
	a dramatic or musical entertainment
	process or manner of functioning or operating