By the simplest definition, two populations are considered as belonging to the same species if they can breed and produce fertile offspring. By that definition, donkeys and horses are not the same species.
I'm not sure about the cats and wild cats. I had a cat that I suspected was a product of a domestic/wild breeding--whenever she would become emotional, her fur would raise up along her spine in a way that I have never seen in another cat. Her kittens (she managed one litter before we had her spayed) all looked like ordinary cats, though.
It's so recent that their kits all behave in the same way ~ and humans find tiger cubs as endearing as the cubs of any other cat ~