break off vs detach

break off and detach both are verbs.

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

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

break off (verb)	detach (verb)
prevent completion	come to be detached
interrupt before its natural or planned end	cause to become detached or separated; take off
break a small piece off from	separate (a small unit) from a larger, especially for a special assignment
break off (a piece from a whole)
break a piece from a whole