stay away vs keep one's hands off

stay away and keep one's hands off both are verbs.

Word	Noun	Adjective	Verb	Adverb
stay away	No	No	Yes	No
keep one's hands off	No	No	Yes	No

As verbs, stay away and keep one's hands off are synonyms defined as:

Other synonyms of stay away include keep one's distance, keep one's eyes off, stand back.

stay away (verb)	keep one's hands off (verb)
stay clear of, avoid	stay clear of, avoid