keep one's eyes off vs keep one's distance

keep one's eyes off and keep one's distance both are verbs.

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

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

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

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