reciprocity vs give-and-take

reciprocity and give-and-take both are nouns.

Word	Noun	Adjective	Verb	Adverb
reciprocity	Yes	No	No	No
give-and-take	Yes	No	No	No

As nouns, give-and-take is a hypernym of reciprocity; that is, give-and-take is a word with a broader meaning than reciprocity:

reciprocity: mutual exchange of commercial or other privileges
give-and-take: mutual interaction; the activity of reciprocating or exchanging (especially information)

Other hypernyms of reciprocity include interchange, reciprocation.

reciprocity (noun)	give-and-take (noun)
mutual exchange of commercial or other privileges	mutual interaction; the activity of reciprocating or exchanging (especially information)
a relation of mutual dependence or action or influence	an exchange of views on some topic
	light teasing repartee