unstable vs mentally ill

unstable and mentally ill both are adjectives.

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

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

Other synonyms of unstable include unsound.

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