Many Orthodox believers will feel the need to explain the discrepancy, and I've heard some well-meaning Serbs even grumble about having to explain to their children "the whole two Christmases thing". But there are no "two Christmases", no "Serbian Christmas" or - as the above series of truly wonderful videos erroneously states - "Russian Christmas." There is just Christmas.
Simply put, today is December 25, 2014 - according to the calendar that was in effect at the time of the Church's founding. Most (though not all) Orthodox churches have refused, for reasons of faith and principle, to accept the modified calendar created by the Bishop of Rome (aka "the Pope" - whom they consider a renegade) in the 16th century. Eventually, most Western countries adopted Pope Gregory's calendar, and - through colonialism and globalization - it became the "secular standard".
The thing about Orthodoxy is that it doesn't care about secular standardization, trends or passing fancies. Because of this, it has endured horrific persecution by Catholics, Muslims, Protestants and atheists - and survived.
Here is an excerpt from this year's Christmas message by the Patriarch of Moscow and All Rus, Kirill:
At the bottom of all conflict, hatred and division is sin. According to St. Justin Popović, sin ‘exploits all its power to accomplish one thing: to render the human person godless and inhuman’ (St. Justin Popović, Philosophical Abysses). And we see in what infernal state the human person at times abides when he has lost the dignity granted to him by the Creator.So, as the Orthodox would say: Christ is Born - Glorify Him!
Yet the Church in the name of God, tirelessly proclaiming to people the ‘great joy’ (Luke 2:10) of the birth of the Saviour, calls upon each dweller on earth to believe and transform himself for the better. She offers to us the way of ascent: from seeking out God to the knowledge of God, from the knowledge of God to communion with God, and from communion with God to becoming like God [...]
In congratulating you all on the great feast of the Nativity of Christ and the New Year I would like to wish you from the bottom of my heart good health, peace, prosperity and abundant succour from on high in following our Lord and Saviour without stumbling.