stay away vs keep one's eyes off

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

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

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

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

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