Tracing back to history, there is evidence that the remains of humans and cats were buried together 9,500 years ago, and that Chinese cats appeared in human homes about 5,300 years ago, eating leftovers and catching mice.
In other words, dogs have been around us for 40,000 years. Humans keep dogs to help with hunting and grazing, but no one has domesticated cats to do these things.
Scientists analyzed their DNA and concluded that at least at the genetic level, cats were not domesticated, and domestic cats and wild counterpart DNA were almost identical.
As we have seen, the dog has got rid of many of the behavior of the wolf, but the cat at home has retained some wildness.