The issue with the way the NYS P/P Law is dealt with on the Gov't side is that each County and sometimes Metro PD is the issuing authority,,not the State of NY.
Though the P/P reads NYS, you get the permit by the grace of the Judge or Police Official of the County or Metro area you happen to live in.

NYSP keeps the sale/transfer records which are a mess and always have been.
But each local jusristiction that actually issued the permit is the one that the permit holder is tied to for adding, deleting guns from the permit,,and the permit holder is also at the opinion of the issuing auth (Judge, PD Cheif, ect) as to wether a concealed carry permit will be issued. Or the permit will be issued with restrictions printed on it such as 'For Target Shooting Only' For hunting only' ,,Not for Concealed Carry.
Some countys judges have even enforced a specific number of handguns allowed on a citizens permit at one time.
Got 5 and want another?,,Then sell one because the issuing auth only allows 5.

Another Judge in an ajoining County may simply issue all the P/P's that come accross his/her desk for final signiture as Concealed Carry.
Depends on the Politics of the issuing auth.

Of course the Judges change and County politics change.
So a 'good' County can become a 'bad 'County' to get a P/P in.
NYS allowed residents to 'shop for P/P's a few yrs ago and lifted the residence in a specific County for application of a NYS P/P.
(Maybe some still follow the old rule of county of residence only.)
So a lot of metro area people often go outside the county to apply in another less restrictive County.(as far as carry restrictions, # of pistols on permit, ect)
When I got my NYS P/P I was 17y/o. The legal age at the time for a NYS P/P was 16.
This was pre GCA 68.
When GCA went into effect I couldn't buy any handguns ( from a FFL) till I turned 21.
My P/P never had any restrictions on it, alwys said concealed carry. But i have seen some peoples P/P's that they have turned in for address updates (yes you have to surrender the P/P for that).
When they recv'd the new one in the mail with the new address, there were also new restrictions printed on the P/P that hadn't been there on the orig.
Concealed Carry is the one that was generally scratched.
New Judge,,a different one than the one that orig Ok'd and signed the orig P/P,,,,,new ideas about how you the citizen should be allowed to express your 2A rights.

All this because the Issuing Authority is the local County Judge, sometimes a State Supreme Court Judge, in some juristictions the Metro PD Chief or Commisioner.
It's not a 'Shall Issue' situation where if there's no legal reason you can't have and carry a pistol, the pistol permit won't be denied. That has been challenged and beaten in several states of late.

NYS has always been since the Sullivan Act went into effect where the citizen had to plead his/her case for the 'need' of a handgun. If that need was sufficient in the eyes of the issuing authority of NYS P/P,,then a P/P would be issued to that person.
If the politics of the time and region said no, then you might as well not even bother trying to apply. It can be a very expensive process.

It's not just about concealed carry either.

Mere possession of a handgun in NYS that is not registered to you on a valid NYS P/P is against the NYS law (NYS Penal Law sec400 ,,long boring reading but it's all right there.)
You need a NYS P/P to have Gramps bringback from the War in a sock drawer in the attic bedroom.
A Colt SAA from the Custer era must be registered and on a NYS P/P or it's an illegal handgun under NYS law. It can be confiscated. Under NYS Law it will be designated a 'Nuisance Firearm' after 1 yr in Police Property and at that time be taken over by the NYSP and destroyed.

This Supreme Court challenge isn't just about NYC gun law, it's about the entire NYState Pistol permit law and how it's applied.