unstable vs unsound

unstable and unsound both are adjectives.

Word	Noun	Adjective	Verb	Adverb
unstable	No	Yes	No	No
unsound	No	Yes	No	No

As adjectives, unstable and unsound are synonyms defined as:

Other synonyms of unstable include mentally ill.

unstable (adjective)	unsound (adjective)
lacking stability or fixity or firmness	not sound financially
subject to change; variable	not in good condition; damaged or decayed
suffering from severe mental illness	suffering from severe mental illness
disposed to psychological variability	containing or based on a fallacy
highly or violently reactive	physically unsound or diseased
affording no ease or reassurance	of e.g. advice