detach vs break off

detach and break off both are verbs.

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

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

Other hyponyms of detach include break, snap off, unbind, unhook.

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