In case anyone is wondering, the issue with Dec 25 v. Jan 6, is this.
In the 1500s, the Church realized that Julius’s calendar which assumed a solar year to be 365 1/4 days, was off by a bit, and that Easter was no longer falling out right. In 1582, Gregory adopted the current calendar, which has a leap year slightly less often, skipping 3 Julian leap years every 400 years. This made the calendar work, but they still needed to do something about the 10 days that their calendar was now off.
So they skipped 10 days. Different counties skipped the days at different times in history, with the Russians only doing it in 1917 after the revolution.
Now, the real issue is that while Pope Gregory did legislate is new calendar into the Roman Catholic Church and its holidays followed his new calendar, he had no authority over the Orthodox churches, and they have not accepted the change.
Therefore, in Roman Catholic churches, the holiday is celebrated on Dec. 25, while in Orthodox churches, it is celebrated on Jan. 6.
Following that, chassidim from countries with an Orthodox church (Russia), observe nittel nacht on Jan 6 which is “their” xmas.