Some pets coexist very peacefully as if they come from the same species. Yet others are in a perpetual cold war while others seem to adopt a policy of live and let live. I have seen some pets like cats and dogs live like bosom friends. It is not uncommon to find a cat lying on a dog oblivious of each others' separate identity. In my place, cats and dogs have adopted a policy of live and let live and occasional closeness save for some minor turf skirmishes over a piece of steak.
We had a mix of pets for a period of 5 years when a pigeon was co-existing with the dogs. They are all staying inside the house, the dogs on the ground floor while the pigeon on the second floor. At first, the dogs chased the pigeon playfully. But when the pigeon showed its muscle by going on a fighting stance, the dogs were stymied. When I bring the dogs out to the front yard, the pigeon would go out too as if she is part of the herd - we have 3 dogs when the pigeon left us.
We have two dogs with two different personalities. The younger one is hyper and loves to play while the older one was spoiled and has an attitude but is quite smart. The older dog would sometimes just attack the other even though she's doing nothing to her. Sometimes the younger one would annoy the older dog because she wanted to play. They have the usual every day war that dogs usually have if they're not both asleep.