Well, yes, but everyone celebrates the same Christmas. Or rather, everyone but the Orthodox who still celebrate it on the Julian calendar, but if that’s relevant, you might indeed refer to “eastern Christmas” and “western Christmas”. But while most nations celebrate some sort of New Year’s festival, it’s not the same New Year’s festival for all of them. Do you mean the European solar new year, or the Islamic lunar new year, or the Jewish solunar new year, or the pan-Asian solunar new year? Or maybe the Thai-specific solunar new year, or the Thai-specific sidereal new year, that septimus mentioned?
The formula is not based on Passover.
"The formula for calculating Easter was set down at the Council of Nicaea in 325…:
Easter is the first Sunday that follows the paschal full moon, which is the full moon that falls on or after the spring equinox.
For calculation purposes, the full moon is always set at the 14th day of the lunar month (the lunar month begins with the new moon). This is called the ecclesiastical full moon; the astronomical full moon may fall a day or so after or before the ecclesiastical full moon."