give up vs leave off

give up and leave off both are verbs.

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

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

give up (verb)	leave off (verb)
stop maintaining or insisting on; of ideas or claims	cease to use
give up in the face of defeat of lacking hope; admit defeat	prevent from being included or considered or accepted
give up or agree to forgo to the power or possession of another	come to an end, stop or cease
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