>>1903069I know the map is Budapest but my first thought was something similar to Berlin and a couple other German cities. There is the U-Bahn and S-Bahn.
U-Bahn is equal to a subway/metro system that is usually underground and only really exists to serve a limited distance from a city centre.
S-Bahn is a regular train, which is a bit of a mixture of an inner city heavy rail form system like a subway - but which is also a mixture of a commuter train. When in the inner sections of a city, they tend to run on busy inner corridors (usually above ground) with fairly good frequency, but then which branch out the further the rail line reaches into the suburbs with stations slowly becoming more distant from each other. This form of transit is not commonly found in North America with some exceptions due to the differences in how the cities are built there, but it is more commonly found in Europe or Asian cities. There are some exceptions, for example New York City or most of that corridor in the USA or certain Canadian examples, such as the systems in Montreal or Ottawa.
Unsure what they mean by heavy rail...I'm guessing just regular old heavy passenger rail between cities.