regret vs unhappiness

regret and unhappiness both are nouns.

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

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

Other hypernyms of regret include sadness.

regret (noun)	unhappiness (noun)
sadness associated with some wrong done or some disappointment	emotions experienced when not in a state of well-being
	state characterized by emotions ranging from mild discontentment to deep grief

regret (verb)	unhappiness (verb)
decline formally or politely
express with regret
feel remorse for; feel sorry for; be contrite about
feel sad about the loss or absence of