Is your ticket a Sparpreis or a Flexpreis ?

A Flexpreis is flexible and is valid for all trains on the day of departure, irrespective of delays/cancellations, etc..
A Sparpreis is bound to the train you bought, if the trains is cancelled or delayed more than 20 minutes, it becomes flexible. In this case, well, your trains is cancelled but replaced by one exactly at the same time. So in theory I think you can change trains if you have a Sparpreis ticket. But if it was me I would not do it, I am not sure that would actually be allowed.