give up vs abandon

give up is not a noun while abandon is a noun.

Word	Noun	Adjective	Verb	Adverb
give up	No	No	Yes	No
abandon	Yes	No	Yes	No

As verbs, give up and abandon are synonyms defined as:

give up and abandon: stop maintaining or insisting on; of ideas or claims

As verbs, give up and abandon are synonyms defined as:

As verbs, abandon is a hypernym of give up; that is, abandon is a word with a broader meaning than give up:

give up: lose (something) or lose the right to (something) by some error, offense, or crime
abandon: forsake, leave behind

give up (noun)	abandon (noun)
	the trait of lacking restraint or control; reckless freedom from inhibition or worry
	a feeling of extreme emotional intensity

give up (verb)	abandon (verb)
stop maintaining or insisting on; of ideas or claims	leave someone who needs or counts on you; leave in the lurch
give up in the face of defeat of lacking hope; admit defeat	stop maintaining or insisting on; of ideas or claims
give up or agree to forgo to the power or possession of another	leave behind empty; move out of
stop consuming	forsake, leave behind
give up with the intent of never claiming again	give up with the intent of never claiming again
relinquish possession or control over
lose (something) or lose the right to (something) by some error, offense, or crime
part with a possession or right
give up what is not strictly needed
allow the other (baseball) team to score
leave (a job, post, or position) voluntarily
put an end to a state or an activity