We have a dog. One of our neighbors some doors away have a cat. It is quite a friendly animal and enjoys a stroke if you have the time to spare.
It seems to have decided to visit our dog from time to time and sits on the windowsill outside whilst the dog barks and whines at it from inside. From time to time it dabs at the dogs nose through the glass.
The other evening the dog decided it wanted a walk after dark and we set off, equipped with doggie bags and a torch to see the inevitable droppings. Along the way, the dog paused to sniff at something dark. I let her sniff for a time. As it was dark, I couldn't make out what the dark patch was so I got the torch out and found it was the cat, stretched out in a relaxed manner on the ground and gently dabbing at the dogs nose - claws retracted - as she sniffed away. Both seemed utterly relaxed in each other's presence.
This behaviour is quite alien to the dogs usual reaction to cats, which a lot less benign to put it mildly.
I suspect its because the cat seems to have no fear of the dog. Were it to run away, the dog would no doubt be off like a shot in hot pursuit.