Despite having the same date, these days hardly ever coincide. That's because they use different calendars. The Jewish calendar is based on precalculated starts to the months, much like the Gregorian calendar. The Biblical calendar uses the sighting of the crescent moon to determine months and leap months added when the barley is still not mature at the end of the 12th month. (The first month of the year requires ripe barley for the wave sheaf ceremony mentioned in Leviticus 23:11-12). This results in the true first day of the 7th month (Day of Trumpets) coming in most years a day or two after Rosh HaShanah is celebrated as the first day of the 7th month.
