The Romans had a 10 month calendar that started with March. Then later they added January and February to better match the lunar cycles in a year. Hence the mismatch of the numbered months.
They had something like ten non-month holy days that the consoles were responsible for sticking in the calendar. This traditionally corrected for the drift. In the political turmoil leading up to to ceasar, this didn't get done. When ceasar imposed the new calendar, he had to insert like 40 extra days to the first year in orderto correct this.