This is an oversimplified answer, but, in a nutshell...
SHALL issue means that as long as you meet the requirements for a permit (i.e. age, no criminal history, maybe a training class - the requirements vary from state to state) then you shall be issued a permit.
MAY issue means you have to make your case as to WHY you need a permit and then you may get a yes or a you may get a no depending on whether or not the judge (or whoever is responsible for the approval of your permit) likes your reason for needing a permit.
NJ is a MAY issue state.. on paper at least.