misery vs unhappiness

misery and unhappiness both are nouns.

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

As nouns, unhappiness is a hypernym of misery; that is, unhappiness is a word with a broader meaning than misery:

Other hypernyms of misery include sadness.

misery (noun)	unhappiness (noun)
a feeling of intense unhappiness	emotions experienced when not in a state of well-being
a state of ill-being due to affliction or misfortune	state characterized by emotions ranging from mild discontentment to deep grief