https://www.state.nj.us/dep/fgw/blueclaw.htm
The shellfish license is for clams/scallops/mussels etc.. It doesn't apply to blue crabs.
I think you need like a $2 permit if you are going to use pots for crabs, but not if you use handlines or box traps.. I will let the guys that go crabbing a lot answer for certain... I think the limit is one bushel.. bob