keep one's hands off vs keep one's distance

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

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

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

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

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