stay off vs keep off

stay off and keep off both are verbs.

Word	Noun	Adjective	Verb	Adverb
stay off	No	No	Yes	No
keep off	No	No	Yes	No

As verbs, stay off and keep off are synonyms defined as:

stay off (verb)	keep off (verb)
refrain from entering or walking onto	refrain from entering or walking onto
	refrain from certain foods or beverages