flake vs break off

flake is a noun but break off is not a noun.

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

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

Other hypernyms of flake include break away, chip, chip off, come off.

flake (noun)	break off (noun)
a small fragment of something broken off from the whole
a person with an unusual or odd personality
a crystal of snow

flake (verb)	break off (verb)
come off in flakes or thin small pieces	prevent completion
cover with flakes or as if with flakes	interrupt before its natural or planned end
form into flakes	break a small piece off from
	break off (a piece from a whole)
	break a piece from a whole