The Deutsche Bahn website, of course, shows a lot, but still not everything. It does not show local public transport tariffs, and local tickets will also have to be bought from regional transport associations.
Federal railway fares apply if you are traveling to another region. Therefore, it may turn out that traveling with the family for 10 minutes to a neighboring city will take as much money as 40 minutes to a neighboring region, because Deutsche Bahn included children in an adult ticket, but local public transport system requires ticket for them.