In New Jersey commercial motor vehicles (CMV) are regulated by the NJ State Police. NJ State Police regulations at NJAC 13:60-2.1(d)1 require any CMV 10,001 pounds or more with a gross vehicle weight rating, registered weight, or combination weight rating (meaning vehicle and trailer) must obtain a USDOT number. The 10,001 pound threshold is met if any one of the three GVWR, registered weight , or combination is met. To obtain a USDOT number you must file a MCS150 and that must be updated every two years. Anyone who drives a CMV with a USDOT number must have an annual USDOT physical from a USDOT approved doctor and is governed by the drivers hours of service regulations.
UCR is the Unified Carrier Registration (UCR). The UCR assess fees to provide for highway safety and enforcement. If you have a USDOT number you must participate in the UCR, even if your state doesn’t participate directly, which is the case with NJ. See pages 9 and 10 of the link.