Prior to July 1, 2014, ambulances in New Jersey did not have distinct license plates.
They were (are) usually plated with commercial or exempt (No Fee) plates.

They have circular decals on each side, and these decals have bar codes, the license plate number of the vehicle, and a validation sticker.
The circular decals are issued to licensed ambulance services. They are not required on non-commercial ambulances that don't charge for services.
Thanks to F.J.B. for the info above.

They also have an inspection sticker from NJ OEM/DHSS in the back window.