The story
The same Nativity, kept on the older calendar. When Pope Gregory reformed the calendar in 1582 the Orthodox churches stayed with the Julian year, and the gap has grown to thirteen days. Russia's civil calendar changed in 1918 but the Church did not, so Christmas falls after the secular New Year, and the Soviet years moved the tree and the presents to New Year's Eve, where they have stayed; Christmas itself became a public holiday again in 1991.
Ethiopia keeps the day as Genna, and at Lalibela the pilgrims in white fill the rock-hewn churches for the night; in Serbia the family brings an oak branch (badnjak) into the house on the eve and burns it.
