New Year's Day - 1 January - arguably the largest celebration of the year. Most of the traditions that were originally associated with Christmas in Russia (Father Frost, a decorated fir-tree) moved to New Year's Eve after the Revolution and are associated with New Year's Eve to this day.
Old New Year - 13 or 14 January (varies) - is an informal traditional Slavic Orthodox holiday, celebrated as the start of the New Year by the Julian calendar.