Khaine = Murder/Assassination/Strategic war
Khorne = Battle/Destruction/Genocide
While similar Khaine is NOT the same as Khorne. Khaine embodies carefully planned murder and ritualistic bloodletting and sacrifice. Khorne is simply destruction and battle for the sake of itself. Think of the difference in the typical offerings to either god: Khaine demands blood, whereas Khorne demands skulls. Khaine is more subtle than Khorne.
Now if you wanna look at WH:40K lore you see that during the Fall of the Eldar, Khaine was one of the few of the Elven pantheon that survived the birth of Slaanesh, but he was severely weakened. Khorne saw Khaine as a useful tool to add to his repertoire so he fought Slaanesh for the right to "own" Khaine. So in 40K lore at least we can see that indeed Khaine has never been, is not, and never will be the same entity as Khorne despite similarities.