The trains connecting German cities are called Intercity (IC) trains and the ones connecting German cities with neighboring countries are called EuroCity (EC) trains.
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As Germany's largest railway company, you're likely to board a Deutsche Bahn service at some point if you're travelling around the country. Offering both high-speed, long-distance services as well as regional routes, travelling by train with Deutsche Bahn is one of the most convenient ways to get around.
Rapid transit or mass rapid transit (MRT), also known as heavy rail or metro, is a type of high-capacity public transport that is generally built in urban areas. A rapid transit system that primarily or traditionally runs below the surface may be called a subway, tube, or underground.