Confusion with two backup drives

I had been doing time machine backups on one external drive that's part of our entire home system, probably in a Cloud, when I started getting notices that backups weren't working. I hooked up a new, physical drive via USB, and went through the steps of starting it. As far as I can determine, it is functioning correctly. However, I've begun getting error notices about the other one not backing up. Since the newer one seems to be making regular backups, can I just ignore these messages? I assume there's a way to designate the newer one as the only drive to be used for backups. Because the other one may be serving some function unrelated to my Mac but to other computers in the house, I don't want to do anything to disable it, just to be sure that it isn't causing any problems.