A officer punitive discharge is called a dismissal and has the same effect as a dishonorable discharge.
In any event, the evidence suggests Kerry was administratively, not punitively, discharged involuntarily. The reason for the action is not clear from the records. That seems to be what Kerry is hiding.
The "Sun" is guessing that Nixon might have arranged a less than honorable discharge. The easiest grounds to prove would be absent for more than three months (as in travelling to Paris).
I like this line of speculation because it explains the frenzy to claim Bush was AWOL.