There are four types of short-distance trains. RE Regional Express provides fast transportation between the centres and the surrounding regions. The term SE is going to be replaced by the term RE in the next years. In general, these trains stop at all stations. These train types are a bit mixed up on some lines so you better look at the train times to determine, if a train is really is a fast or a local train.
Most railway lines have a train every two hours, every hour or two times an hour.
Most S-Bahn lines run every 15 to 40 minutes in the suburbs and every 2 to 20 minutes in the urban cores. New urban railway networks are planned or under construction in Hannover and Mannheim. A number of cities decided to gradually put their tramway network under ground instead of building a complete new subway system. Some lines now have all features of a subway, but there are still tramays in most of the tunnels. Essen has Duo-Buses, but the electric part of the system is closed, due to derailing problems of the trolley poles and problems with the wooden bus track in the tramway tunnel.