fight off vs fight back

fight off and fight back both are verbs.

Word	Noun	Adjective	Verb	Adverb
fight off	No	No	Yes	No
fight back	No	No	Yes	No

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

Other hypernyms of fight off include defend, fight, fight down, oppose.

fight off (verb)	fight back (verb)
force or drive back	fight against or resist strongly
	defend oneself