extermination vs destruction

extermination and destruction both are nouns.

Word	Noun	Adjective	Verb	Adverb
extermination	Yes	No	No	No
destruction	Yes	No	No	No

As nouns, destruction is a hypernym of extermination; that is, destruction is a word with a broader meaning than extermination:

extermination: the act of exterminating
destruction: the termination of something by causing so much damage to it that it cannot be repaired or no longer exists

Other hypernyms of extermination include devastation.

extermination (noun)	destruction (noun)
the act of exterminating	the termination of something by causing so much damage to it that it cannot be repaired or no longer exists
complete annihilation	an event that completely destroys something
	a final state