King Daniel wrote:
^They're the same character.
Given that they were raised in completely different universes, and one of them is over a decade older than the other, how are they "the same." Certainly not the same in knowledge, experience and skills. They are two entirely different people, who just happen to share the same name.
About the only thing we know about the alternate McCoy's skills as a doctor is that apparently he doesn't understand how to administer an injection.
They're two different actors playing the same ficticious character. Don't confuse the age of the actor with that of the character. In-universe, they are the same, just as Kirsty Alley and Robin Curtis are both Saavik.