If you have a pistol legally in NJ, it means you have a NJ Firearms Purchaser ID card and had a pistol permit form. For each handgun one wishes to purchase in the state of NJ, a separate form is required (normally with a separate background check and letter to your employer asking them if you can be trusted with firearms/handguns...no, I'm not kidding!) and depending on where one lives, one to sic handgun permits may be obtained at one time. One has 90 days to use said handgun purchase permit before it expires or is renewed, at the discretion of the Chief of Police or clerk, for a further 90 days. Depending upon where one lives, unused forms may or may not be required to be returned to the clerk.
For long guns, be they rifle or shotgun, all you need is your valid ID (driver's license) and you NJ Firearms Purchaser ID card. This holds true in states with reciprocity, like PA, OH, IA.