There calendar has its own date, which we have figured out corresponds to our calendar. Each day the sun rises is a new day, you could "call' it anything, call it "next Monday" or call it "10 Ahau" or call it "November 12", it is still the same day. The following day would be called "next Tuesday" or "11 Ahau" or "November 13." It is still just the next day no matter what you label it.

The naming convention varies with the culture, but the days are sequentially ordered throughout the centuries and exist in reality. WE humans choose what to call or name the days.

The Mayans called certain days by one name and we called the same exact days by a different name.

On the day that WE call December 21, 2012, the Mayans call it 13.0.0.0.0., the end of the 13th Baktun. End.