Upvote:4
"On the booked route" is the key here. The route does not only include start and destination, but also routing instructions (German term "Wegevorschrift", VIA on the ticket).
The routing instruction may look something like this for ticket from Konstanz to Karlsruhe: VIA: SIN*(OG/S).
In this example, you need to go via Singen, and may then either a route via Offenburg or via Stuttgart.
For a list of abbreviations on this VIA, see here. If this link dies at some point, search for Leitpunktkuerzel.
In your specific example, your cheaper ticket will likely have a routing instruction that says you must indeed take the route that goes through Koblenz. It is not impossible that the more expensive ticket allows both routes, but I doubt it.
It should be possible to pay the the fare difference at a Deutsche Bahn ticket desk if you already have a ticket and decide to change the route.