forgoing vs giving up

forgoing and giving up both are nouns.

Word	Noun	Adjective	Verb	Adverb
forgoing	Yes	No	No	No
giving up	Yes	No	No	No

As nouns, giving up is a hyponym of forgoing; that is, giving up is a word with a more specific, narrower meaning than forgoing:

forgoing: the act of renouncing; sacrificing or giving up or surrendering (a possession or right or title or privilege etc.)
giving up: the act of forsaking

Other hyponyms of forgoing include forsaking, abnegation, denial, self-abnegation, self-denial, self-renunciation.

forgoing (noun)	giving up (noun)
the act of renouncing; sacrificing or giving up or surrendering (a possession or right or title or privilege etc.)	the act of forsaking
	a verbal act of admitting defeat