Most of the trains on the Oresundtrain network are operated by DSB Øresund, a joint operation between DSB and First Group, and Veolia but a few are operated by DSB on the inter-city line to Ystad, where they connect to the high-speed ferry to Bornholm.
There are of course trains that are something in between regional and inter-city, like the Oresundtrain (between Copenhagen and 3 cities in Sweden over 3 hours away) with stopping pattern like a regional train and pass prices attracting work commuters.