It's a concealed carry permit. P would not be for protection as that right is already provided under PL Article 35 and 265. You may carry loaded and concealed from the time you leave your home until you return from any of these activities.
Once again, please don't confuse NYS with NYC. Trust me, most who think NYS is bad have only one thing over on us; we're a discretionary issue state. Yet of the thousands of students I've trained, only one has ever been denied a permit. And an unrestricted carry permit is generally possible by taking one of many approaches. Once issued our carry rights trump many so called gun-friendly states. We can carry in a bar, restaurant, hospitals, churches, banks, on public transportation, public lands and the permit never need be renewed. We remain pretty much unmolested. I keep reading about these restricted areas in state after state. NY permits are good for life unless revoked for cause.
The permit restrictions described are pretty close to an unrestricted. I recently had a student receive an unrestricted right from the start. The judge advised him he doesn't usually do this until the permit holder has some experience. He made the exception because the student took extra concealed carry training before filing his application.
Call Maureen at the pistol permit department. She's very nice and will explain the coding for you. Then PM me, I believe the restrictions can be lifted entirely.