So when I played first, the reserve was always sorted in a way where creatures came one after the other, first all the Dragons, then all the Rocs, then the Gryphons etc.

Now when I started playing again I noticed that it was suddenly different, it sorted creatures by when I put them into the Reserve, first the oldest pets and last the ones I just recently put in. I was rather miffed by this change, but put up with it, not seeing any way to change it back.

Now suddenly, while going through my Reserve pets, it switched and is now sorted by species again. How did this happen? Did I click something by accident? Am I just missing something and can you somehow choose how to display pets? Would this work for the Stable too? 

There is no way to change the type of pet ordering right now, and there are was no special system in ordering pets in reserve, so they were output in the order how they were pulled from database. We added the sorting by species and then by name. Pets in Stables are ordered first by level and then by name.