Looking at the Immigration Bureau website, I see that the embarkation/disembarkation card for foreign residents will yet again change design from July (pdf).
Instead of just ticking a box for "deemed reentry permit" you will now be asked to tick boxes to choose between deemed reentry permit or reentry permit by application. As usual the English is ambiguous: what they call special permission is in fact the one which you did not go to specially apply for, but is the one you got by default...