Aveline, my two sit around companionly doing nothing as far as I can see, then disappear together presumably taken a census of the local mouse population!
I have known dogs too, that detested one particular dog on sight, or made friends immediately with a strange dog.
We had a blackbird in the garden who apparently was on friendly terms with both cats - neither of whom were card carrying members of the society for the protection of birds. As far as I know the blackbird died of old age.
I have even heard of a fox terrier that had a friend that was a rat!
In the dire frost and snow in February, a small bird chose to live in the workshop and risk being caught by the cat, rather than risk freezing to death outside overnight.