wear off vs wear down

wear off and wear down both are verbs.

Word	Noun	Adjective	Verb	Adverb
wear off	No	No	Yes	No
wear down	No	No	Yes	No

As verbs, wear off and wear down are synonyms defined as:

Other synonyms of wear off include wear, wear out, wear thin.

wear off (verb)	wear down (verb)
deteriorate through use or stress	exhaust or get tired through overuse or great strain or stress
diminish, as by friction	deteriorate through use or stress