give up vs withdraw

give up and withdraw both are verbs.

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

As verbs, withdraw is a hyponym of give up; that is, withdraw is a word with a more specific, narrower meaning than give up:

give up (verb)	withdraw (verb)
stop maintaining or insisting on; of ideas or claims	keep away from others
give up in the face of defeat of lacking hope; admit defeat	remove something concrete, as by lifting, pushing, or taking off, or remove something abstract
give up or agree to forgo to the power or possession of another	make a retreat from an earlier commitment or activity
stop consuming	take back what one has said
give up with the intent of never claiming again	release from something that holds fast, connects, or entangles
relinquish possession or control over	lose interest
lose (something) or lose the right to (something) by some error, offense, or crime	pull back or move away or backward
part with a possession or right	remove (a commodity) from (a supply source)
give up what is not strictly needed	cause to be returned
allow the other (baseball) team to score	break from a meeting or gathering
leave (a job, post, or position) voluntarily	withdraw from active participation
put an end to a state or an activity	retire gracefully