sadness vs unhappiness

sadness and unhappiness both are nouns.

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

As nouns, sadness and unhappiness are synonyms defined as:

sadness and unhappiness: emotions experienced when not in a state of well-being

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

sadness: the state of being sad
unhappiness: state characterized by emotions ranging from mild discontentment to deep grief

sadness (noun)	unhappiness (noun)
the quality of excessive mournfulness and uncheerfulness	emotions experienced when not in a state of well-being
emotions experienced when not in a state of well-being	state characterized by emotions ranging from mild discontentment to deep grief
the state of being sad