fall off vs detach

fall off and detach both are verbs.

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

As verbs, detach is a hypernym of fall off; that is, detach is a word with a broader meaning than fall off:

Other hypernyms of fall off include come away, come off.

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