There are two kinds of Privet that are naturalized in Indiana; Border Privet and European or Common Privet.
They are both non-native plants that were brought over for landscaping purposes. My own experience with them is to find them at the locations of old homesteads or farms. The same sort of places that you find daffodils and wisteria growing. They seem to hang around for a long time after the homes are gone, but don’t spread too much. I’ve read that in other places they’re quite invasive, but not in my experience in northeast Indiana.
The two species are similar. Some differences are:
1. For Border Privet, the smaller twigs and flower stems are hairy, but not in the European Privet.
2. The flower clusters of Border Privet are 1-2 inches in length, while they are usually longer in European Privet.
3. The flower tubes of the Border Privet are long, twice as long as the petals, while in the European Privet they are about the same length as the petals.