How true is this? Are there countries that use a different calendar aside the one we use?

13 months in a year?

Yes, in fact here in Africa
There are many cultures around the world that have and follow their own calendars, which is exactly not the same as the Western Gregorian calendar. However, despite that, they abide by the rule of 12 months a year. An Ethiopian year is comprised of 13 months and is seven years behind the Gregorian calendar. In fact, Ethiopians celebrated the new millennium on September 11, 2007; this is because the Ethiopians continued with the same calendar that the Roman church amended in 525 AD. While the first 12 months have 30 days, the last month, called Pagume, has five days and six days in a leap year.

Till date, Ethiopia uses its ancient calendar, which hardly creates any inconvenience for travellers because of the calendar difference. However, most Ethiopians these days are now aware of the Gregorian calendar, and some even use both calendars interchangeably.

Ethiopia, being one of the few countries in the world, still uses its own calendar system. The country celebrates some important holidays on days that are different from the rest of the world.