come off vs fall off

come off and fall off both are verbs.

Word	Noun	Adjective	Verb	Adverb
come off	No	No	Yes	No
fall off	No	No	Yes	No

As verbs, fall off is a hyponym of come off; that is, fall off is a word with a more specific, narrower meaning than come off:

Other hyponyms of come off include blow off, chop off, cut off, lop off, unsolder.

come off (verb)	fall off (verb)
happen in a particular manner	fall heavily or suddenly; decline markedly
come to be detached	diminish in size or intensity
break off (a piece from a whole)	come off