mentally ill vs unstable

mentally ill and unstable both are adjectives.

Word	Noun	Adjective	Verb	Adverb
mentally ill	No	Yes	No	No
unstable	No	Yes	No	No

As adjectives, mentally ill and unstable are synonyms defined as:

Other synonyms of mentally ill include unsound.

mentally ill (adjective)	unstable (adjective)
suffering from severe mental illness	lacking stability or fixity or firmness
	subject to change; variable
	suffering from severe mental illness
	disposed to psychological variability
	highly or violently reactive
	affording no ease or reassurance