There is a clinical difference between insane and mentally ill. 

An insane person is "so irrational in their behavior, or so unable to control it - so unlike 'us'" that they are not criminally liable (from earlier in the chapter).

Mental illness is "substantial disorder of thought or mood that substantially impairs judgement ..." (from near your link).

Clearly this is a subtle clinical distinction and will hinge on the expert evidence and the applicable law.