Hang on -- an insanity plea (depending on what state we're talking about informs what that entails), is a positive defense. It's an admission of guilt. It doesn't mean no crime was committed; it means the person who committed the crime isn't going to be held responsible for it, because he or she (insert reason related to statute here -- often by reason of disease, person exhibits a lack of understanding of the act/inability to conform behaviour, or lack an understanding of the wrongfulness thereof, depending on the standard used) was insane at the time of the offense.
It doesn't result in commitment; it results in remanding the person to care until such time as they are returned to a state in which they can understand/appreciate and aren't likely to pose a danger to themselves or society. That can be a very short time or a very long time (and is often politically motivated). People have basically walked away from winning insanity pleas; people have spent decades in psychiatric facilities following winning insanity pleas. Insanity pleas remain an incredibly rare thing for any atty to try and an even rarer win.
Diminished capacity is, indeed, specific to jurisdiction, and is used to move (mostly to mitigate) either charges or sentencing.
Also, Hinkley yeah, much better off than if in prison -- he wouldn't have been spending weekends at home for decades from prison. Nor would he likely have gotten out.