misery vs suffering

misery and suffering both are nouns.

Word	Noun	Adjective	Verb	Adverb
misery	Yes	No	No	No
suffering	Yes	Yes	No	No

As nouns, suffering is a hyponym of misery; that is, suffering is a word with a more specific, narrower meaning than misery:

Other hyponyms of misery include concentration camp, living death, woe.

misery (noun)	suffering (noun)
a feeling of intense unhappiness	feelings of mental or physical pain
a state of ill-being due to affliction or misfortune	psychological suffering
	a state of acute pain
	misery resulting from affliction

misery (adjective)	suffering (adjective)
	troubled by pain or loss
	very unhappy; full of misery