loneliness vs unhappiness

loneliness and unhappiness both are nouns.

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

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

Other hypernyms of loneliness include sadness.

loneliness (noun)	unhappiness (noun)
a disposition toward being alone	emotions experienced when not in a state of well-being
sadness resulting from being forsaken or abandoned	state characterized by emotions ranging from mild discontentment to deep grief
the state of being alone in solitary isolation