you're partally right... DUI's are criminal cases, not just traffic cases. IIRC, a DUI is on a TRAFFIC record for either 3 or 7 years but I cannot remember exactly... after that they do expire off your driving record after that time like a speeding ticket would but the DUI remains on the CRIMINAL record for life.
Generally for a first time DUI case, a person gets their license restricted to essential business, and has to go to AA or similar classes and provided that they complete those classes the DUI will be off the criminal record and be treated solely as a driving infraction and thus expires when the statue expires.
Not an expert in US law, but depending upon the circumstances of the DUI/DWI offense, it could be classified as either a misdeamoner or a felony. While this classification makes a difference in the USA, in many countries, including Canada, any DUI/DWI is counted as a Criminal Code conviction equivalent to a felony and generally bars someone with such a conviction from entering the country. So, DUI/DWI can have serious implications for international travel. Many Americans do not realize this until some event causes their background to be checked at a border entry point and "boom", barred from entry, noted in the computer records as failure to declare criminal conviction and big trouble getting across the border in the future.