Does the moon have anything to do with months?
There are 12.36 lunar months in one Greogorian year [nearly same for solar year], since lunar month consists of 29.53 days. However there are only 13 lunar months if at all it is a lunar year.12 lunar months are a bit shorther than a "solar year" - about 11 days shorter. In the case of the Islamic calendar, what they call year is by definition exactly 12 lunar months - but this year is shorter than a year of the Gregorian calendar, by about 11 days.