giving up vs relinquishment

giving up and relinquishment both are nouns.

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

As nouns, relinquishment is a hypernym of giving up; that is, relinquishment is a word with a broader meaning than giving up:

giving up: a verbal act of admitting defeat
relinquishment: a verbal act of renouncing a claim or right or position etc.

Other hypernyms of giving up include relinquishing.

giving up (noun)	relinquishment (noun)
the act of forsaking	the act of giving up and abandoning a struggle or task etc.
a verbal act of admitting defeat	a verbal act of renouncing a claim or right or position etc.