The short answer: there is no difference. Generally speaking, DUI stands for driving under the influence, which is a broad label that refers to crimes of intoxicated driving.
Different states have different names for the offense—depending on where you are, it might be called driving while intoxicated (DWI), operating while intoxicated (OWI), operating under the influence (OUI), or other similar variations. When the State of Indiana accuses you of DUI, your formal criminal charge is for operating a vehicle while intoxicated, or OVWI.
In layman’s terms, DUI and OWI are used more-or-less interchangeably across the nation. In some jurisdictions, both charges might exist with varying degrees of seriousness; in others (like Indiana), there’s one umbrella term (OVWI) that encompasses all kinds of intoxicated vehicle operation.
Believe it or not, one of the reasons that Indiana has the OVWI charge is that it’s more expansive and inclusive than DUI—operating is a broader term than driving. Your vehicle doesn’t even need to be in motion for you to be convicted of operating it.
At the end of the day, while there are some distinctions between the alternate names for drunk driving, these differences are usually a function of where you live, and not the nature of the underlying charge. If you or a loved one is involved in an alcohol-related case in Indiana, call the Marc Lopez Law Firm at 317-632-3642, and remember—always plead the 5th!