"Bahn" is the general term and can also refer to the whole rail system, "Zug" is specific for train. You say "Deutsche Bundesbahn" (German Railways), you couldn't say "Deutsche Bundeszug". OTOH, it doesn't make a difference if you say "ich steige in den Zug" oder "ich steige in die Bahn", in the latter case "Bahn" is used for "some specific part of the whole Bahn-system, i.e. a train".

´Bahn´ is also used for the ´S-Bahn (Schnellbahn)´ or ´Straßenbahn´ in Germany. E.g.: ´Ich lebe in Hamburg und benutze jeden Tag die Bahn, um zur Arbeit zu fahren.´ In this case I would not think of a train being used. But: ´Die Fahrt mit dem Zug/mit der Bahn von Berlin nach Hamburg dauert zwei Stunden´ Here everybody thinks of a trip by train.