Christmas (or New Year?) confusion

A hilarious Turkish quirk has come to light over the last two weeks. Whilst the Turks are all aware of Christmas and understand its significance to us as a religious holiday, they seem to believe it to be somehow fused with New Year's Eve, perhaps even believing it to be one and the same thing. Let me explain further. Having had only the most cursory smattering of Christmas propoganda in the run-up to actual Christmas, in the run-up to New Year's Eve, Istanbul was inundated with it. All along the main streets there were cut-outs of Christmas trees and ball-balls, not, however, bearing the usual Christmas greetings, but instead best wishes for 2013. From about the 27th until the 31st there were vendors stationed on every street corner selling Father Christmas hats, shops were playing out the Turkish version of 'Jingle Bells' (which is almost worse than the original version) and on New Year's Eve itself, I even saw someone in full Father Christmas costume! My lovely students all very sweetly wished me a 'Happy Christmas', but not on the 23rd or the 24th, but on the 31st, which prompted me to spend about half an hour of my lesson going into a detailed breakdown of the difference between the two events, using various timelines and diagrams of Christmas trees and fireworks to clarify my meaning.