Same category means category of trains : ICE, EC, RE. S-Bahn, etc ...
So if your ticket for the cancelled train was for ICE you can take any ICE or below (RE, etc ...) to your destination.
If your ticket was for RE/RB, you can take any RE/RB or below to your destination, but not an ICE/EC.

In your case anyway, I had a look and it seems that basically you got caught in Germany love of being precise: this was a reschedule. Your train is still in service but with a different itinerary due to work. It will deserves different station and takes longer. This is in effect a reschedule but for German minds : they cancel the original train service and replace it with one with the same number departing at the same time, so they inform you of the cancellation but not of the replacement. So you have nothing to do, just show up for the train you were scheduled for.

They do the same thing sometime at short minute if they change the rolling stock: they will tell you 45 min your train is cancelled, but not tell you they will replace it with one departing at the exact same time, just a different machine.