give one's best vs do one's best

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

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

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

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

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