? if you mean the Julian vs Gregorian , then the difference was days not years. When the Julian (named after Caesar) was created it had 365 days a year and a leap year every 4 years. The issue, there are just under 365.25 days in a year. At the time of Pope Gregory XIII they realised that things where not falling (spring) when it should, so the great minds at the time moved the days back a few days (so that things fall where they should) and added the new rule that every centurial year (i.e. ...1800,1900,2000,2100...) has to be divisible by 400 to be a leap year. So 1900 was not a leap year and 2100 won't be one (assuming the world is still around) but 2000 was one.

right now there is exactly 13 days difference between the two.

if you mean different ethnic calendars (i.e. Chinese ..... vs common/Gregorian) then yes they can even have millennia differences, but that is irrelevant since the idea comes from the Mayan calendars numbering system and how it pertains to the Common Calendar (don't know if it was ever applied to the Julian) and idiots (i.e. the actual calendar does not stop at that point.)