unsound vs unstable

unsound and unstable both are adjectives.

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

As adjectives, unsound and unstable are synonyms defined as:

Other synonyms of unsound include mentally ill.

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