Well, I'm not necessarily the highest authority on the matter but with the way I understand it these are simply conditions for victory with no stipulation that both people have to win the exact same way. If they did have to do it the exact same way, then that would be really convoluted since the combatants are presumably not negotiating the victory conditions with each other and would therefore not necessarily know what the other person is going for unless it is really blatant and you would also have to clear up if they need to utilize the exact same method for killing or incapacitation as well. So yeah, they have are free to choose independently from the other one since anything else would be impractical as far as I'm concerned.