fight off vs fight down

fight off and fight down both are verbs.

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

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

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

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