The key difference is that nonjudicial punishment generates a paper trail and nonpunitive doesn't.
FORBES: A Few Bad Men
2.
Under military law, nonjudicial punishment is a less severe form of punishment than prosecution.
FORBES: A Few Bad Men
3.
In other words, nonpunitive offenders are treated as first-time offenders if they get in trouble down the road while nonjudicial offenders are treated like recidivists.