give up vs shut off

give up and shut off both are verbs.

Word	Noun	Adjective	Verb	Adverb
give up	No	No	Yes	No
shut off	No	No	Yes	No

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

give up (verb)	shut off (verb)
stop maintaining or insisting on; of ideas or claims	block off the passage through
give up in the face of defeat of lacking hope; admit defeat	isolate or separate
give up or agree to forgo to the power or possession of another	stem the flow of
stop consuming
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