perk vs gratuity

perk and gratuity both are nouns.

Word	Noun	Adjective	Verb	Adverb
perk	Yes	No	Yes	No
gratuity	Yes	No	No	No

As nouns, gratuity is a hyponym of perk; that is, gratuity is a word with a more specific, narrower meaning than perk:

perk: an incidental benefit awarded for certain types of employment (especially if it is regarded as a right)
gratuity: a relatively small amount of money given for services rendered (as by a waiter)

Other hyponyms of perk include apanage, appanage, backsheesh, baksheesh, bakshis, bakshish, pourboire, tip.

perk (noun)	gratuity (noun)
an incidental benefit awarded for certain types of employment (especially if it is regarded as a right)	a relatively small amount of money given for services rendered (as by a waiter)
	an award (as for meritorious service) given without claim or obligation

perk (verb)	gratuity (verb)
gain or regain energy