In the Islamic Calendar, the Hijri, calling a year a sequential number wasn’t the original plan. The years used to be named after significant events of the year. So there was the Year of The Trial, the Year of Permission, The Year of Equality, the Year of the Earthquake. Imagine trying to come up with one single defining feature for each of year now. Boaty McBoatFace, pah!
But it became complicated, and numbering started with the year Mohammed make the pilgrimage from Mecca to Medina - the year 662 CE. That became year 1, so this year, which starts today, is the year 1438. The Hijri calendar starts with the first day of the first month of Muharram. So today is 1 Muharram 1438.
The calendar itself is complex for a number of reasons, but one of the biggest challenges is that the start of each month is decided by the sighting of the Hilal - the crescent moon - by “one or more trustworthy men testifying before a committee of Muslim leaders.” For global interconnectedness reasons that isn’t very practical. Some Muslim countries use a tabular system to pre-determine the month starts. Saudia Arabia uses the sighting of the Hilal system alongside the Umm al-Qura calendar for administrative purposes, and the Gregorian calendar for paying government salaries.
Its unusual, the not unheard of, for Jewish and Islamic New Year to fall at the same time. Both calendars are calculated according to the moon (although the Hebrew calendar is lunisolar, and Islamic just lunar) and both count the day as starting from sundown. Which is interesting in its non-uniformity, unlike the clock based system. I like the seasonal notion of timing of days. A day ends when it gets dark. And, personally, as a fan of breaking up the day with a nap, I’d be pretty happy starting the day in the evening.