do one's best vs give one's best

do one's best and give one's best both are verbs.

Word	Noun	Adjective	Verb	Adverb
do one's best	No	No	Yes	No
give one's best	No	No	Yes	No

As verbs, do one's best and give one's best are synonyms defined as:

Other synonyms of do one's best include give full measure, go all out.

do one's best (verb)	give one's best (verb)
perform a task as well as possible	perform a task as well as possible