derision vs put-down

derision and put-down both are nouns.

Word	Noun	Adjective	Verb	Adverb
derision	Yes	No	No	No
put-down	Yes	No	No	No

As nouns, put-down is a hyponym of derision; that is, put-down is a word with a more specific, narrower meaning than derision:

Other hyponyms of derision include jeer, jeering, mockery, scoff, scoffing, squelch, squelcher, takedown, befooling, stultification.

derision (noun)	put-down (noun)
the act of deriding or treating with contempt	a crushing remark
contemptuous laughter