I have never heard of New Christmas and Old Christmas, but in my later childhood, my mother always celebrated Twelfth Night, with a small and less involved celebration than we had on Christmas. Usually just some special food and eggnog. I know that in Hispanic communities the same night is generally called Three Kings Day and in some countries that is when gifts are exchanged, due to the fact that it took 12 days for the three kings to come after being told of the birth of Jesus, so their gifts were given then not at the beginning as our modern custom seems to have developed.

To further confuse things, my wife was born on December 6, which is Saint Nicholas Day, which is some places is when gifts are brought by Saint Nicholas, not on Christmas which is a much more reverent holiday in the countries where this happens. I find it interesting that so many cultures all celebrate the same holiday, and all exchange gifts, yet do so on different days because of different parts of the same tradition. Sometimes the cynical part of me, says that trying to push all three days into each other is just a way to minimize holiday interruptions to the outside world.