The subject becomes perhaps a little less confusing when you
look at it from a slightly different angle:
The "year" is not what we print on calendars. The "year" is the
time the Earth takes to complete one revolution around the sun ...
roughly 365-1/4 days.
The moon's revolution is not tied to the Earth's revolution in any
way. The moon does its own thing in its own orbit, and shows a
complete set of "phases" in roughly 29.53 days.
The reason so many cultures have made so many different
calendars is because no calendar can exactly match the sun
and the moon with whole numbers of days, and each calendar
tries to come close, in a different way.
Everybody's calendar does the best it can to fit the year.
And every calendar also has some structure that also goes
along with the moon ... some more closely, and some less.
The Gregorian calendar that we use does a very good job
matching the year, and then the "months" kind of give the moon
some recognition without really trying to match it closely.
The Islamic, Hebrew, and Chinese calendars begin their months
with the New Moon. The Islamic religious calendar ... as
I understand it, but I may be wrong ... is strictly lunar. It simply
begins a new year after 12 complete cycles of moon phases.
That makes the Islamic religious calendar about 11 days shorter
than Earth's revolution around the sun, and is the reason why
you'll notice Ramadan starting earlier every year than it did
the year before.
The Hebrew religious calendar is also strictly lunar, but with a big
additional device that brings it into alignment with the year.
The Hebrew religious months begin right on the New Moon,
so 12 of them are about 11 days shorter than a real year.
Then ... seven times in each 19 years ... the Hebrew religious
calendar adds an extra whole month/moon, and has 13 of them
before the next year is counted. This actually does a great job
of matching up with both the sun and the moon. The system
has been in place for over 2000 years, and it has worked out
such that ... without any special tampering ... Passover and
Sukkot (Tabernacles) always begin on the 15th of the month,
which is always the night of the Full Moon that is nearest the
respective Equinoxes.
By the way ... Most Islamic countries use the Islamic calendar for
prayer and religious applications, and the Gregorian calendar for
trade and business dealings. Israel and other Jewish communities
worldwide use the Hebrew calendar for prayer and religious occasions,
and the Gregorian calendar for trade and business dealings.
