detach vs fall off

detach and fall off both are verbs.

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

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

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

detach (verb)	fall off (verb)
come to be detached	fall heavily or suddenly; decline markedly
cause to become detached or separated; take off	diminish in size or intensity
separate (a small unit) from a larger, especially for a special assignment	come off