DUI stands for “Driving Under the Influence” and DWI stands for “Driving While Intoxicated”. They both stand for the same thing; however, in Connecticut, the offense is called DUI. This is because statutorily the offense states “driving under the influence of intoxicating drugs or alcohol”, which means that a person can be charged with a DUI even though they had no alcohol, but was under the influence of drugs, whether prescription or not.