In Judaism, the New Moon ushers in a new month

Rosh Chodesh or Rosh ḥodesh (Hebrew: ראש חודש‎; trans. Beginning of the Month; lit. Head of the Month) is the name for the first day of every month in the Hebrew calendar, marked by the appearance of the new moon. The new moon is marked by the day and hour that the new crescent is observed. It is considered a minor holiday, akin to the intermediate days of Passover and Sukkot.^[1]

An Independence Day is an annual event commemorating the anniversary of a nation's assumption of independent statehood, usually after ceasing to be a colony or part of another nation or state; more rarely after the end of a military occupation.

Most countries observe their respective independence days as a national holiday, and in some cases the observance date is controversial or contested. Not all countries observe an independence day holiday, choosing to celebrate other national days instead of or alongside an independence day.