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

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

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

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

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

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