festival vs festivity

festival and festivity both are nouns.

Word	Noun	Adjective	Verb	Adverb
festival	Yes	No	No	No
festivity	Yes	No	No	No

As nouns, festivity is a hypernym of festival; that is, festivity is a word with a broader meaning than festival:

festival: an organized series of acts and performances (usually in one place)
festivity: any joyous diversion

Other hypernyms of festival include celebration.

festival (noun)	festivity (noun)
an organized series of acts and performances (usually in one place)	any joyous diversion
a day or period of time set aside for feasting and celebration