DUI stands for Driving Under the Influence and refers to drunk driving offenses, while DWI stands for Driving While Intoxicated or Driving While Impaired. In some states, the two terms are both used to describe impaired or drunken driving. However, in states where both terms are used, DWI usually refers to driving while intoxicated of alcohol, while DUI is used when the driver is charged with being under the influence of alcohol or drugs. New Jersey law makes no distinction between a DWI and a DUI.