How does the Ethiopian calendar differ from other calendars in the world and how many calendar systems exist?

I would like to understand how the Ethiopian calendar works and how it differs from the Gregorian calendar used in most of the world. Why is the Ethiopian calendar around seven to eight years behind the Gregorian calendar and what is the historical and religious origin of this difference? How many months does the Ethiopian calendar have and what is the significance of the thirteenth month Pagume? How do Ethiopians celebrate New Year (Enkutatash) and when does it fall in the Gregorian calendar? Beyond the Ethiopian and Gregorian calendars, how many other calendar systems exist in the world today and what are the most widely used ones such as the Islamic, Hebrew, Chinese, and Julian calendars? How do countries and communities that use different calendars manage dates, appointments, and official documents when interacting with the rest of the world?