No one really mentioned a "one-shot stop," but a lot of the controversy about that actually centers around the definition of "stop." It is entirely possible for a human or animal to be shot and go down instantly, then get up and run. I don't know how a case like that would fit into the books. More than anything else it just ruins the neatness of the case files. In any case, a hit on the head will usually put down the individual for at least a minute or two.
I've never seen a person shot but I have seen animals hit in the head fall as if hit in the head with a sledge hammer, which in fact is one way beef cattle are sometimes "put down." The one I saw was shot by a shotgun and I assure you it never got up again. There was, by the way, hardly any visible wounding and hardly any blood but down it went. Chickens, on the other hand, do not go quietly, no matter what you do them.
Fairburn, in his book "Shooting to Live" goes into some detail about how he was less and less sure about stopping power the more he learned and experienced. Basically he said that he became less confident about making blanket statements about stopping power with any measure of assurance. While what he wrote is dated (hollow points were yet to be when he was writing), it is still of interest and mostly relevant. Amont other things, he said the 7.63 Mauser pistol was the most feared round in use where he served (Shanghai, China) but he nevertheless armed most of his police with .45 Colt Automatics. One of his statements was that the more his handguns operated like machine guns, the more he liked it (or words to that effect).
He covered a lot of ground in his book (but left a lot uncovered). Among the other things he mentioned was that anyone with a weapon that he had no training on should turn it in to the police (don't try that yourself). He recommended dry firing practice and for home defense, a double-barrelled, short barrelled, outside rebounding hammer, shotgun--packed full of stopping power.