Dr. Mark Wright noticed that when the resurrected Savior appeared to his disciples in the Old World, John repeats three times that Christ showed first his hands, and then his side. In the New World, Christ showed first his side, then his hands and feet. Wright noted that the wound in the side would show that he died. That understanding tells us why there was such a subtle difference.
In the Old World, all of the disciples knew Christ had died. Many had been there. Thus, when Christ appeared, he didn’t need to demonstrate that he had died, but rather that the living being they saw before them was the very one who had died, hence the marks in the hands.
In the New World, it was very obvious that they saw a living being. They had never known the mortal Christ. Therefore, what was important in the New World was that they understood that this living being had died, and the wound in his side would have clearly spoken to them, revealing to them that the recipient of such a wound had indeed died.
Christ showed each group what they needed to know to fully understand that Christ had actually risen from the dead.