stay away vs keep one's distance

stay away and keep one's distance both are verbs.

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

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

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

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