Theoretically, Easter is the Sunday after (never on) Passover, although some early Christians celebrated Easter on Passover. However, there are five different calendars here, with different hypothetical moons and hypothetical equinoxes.
The Jewish calendar is a lunar calendar of 12/13 months a year.
After the earliest days, most Christians were gentiles, and wanted to use instead the Julian Calendar of Julius Caesar, which was in universal use in the Roman Empire, so they made some calculations for when Passover, and therefore Easter, should fall. This is still used by conservative Eastern Orthodox Christians, who believe that ancient tradition is more important than astronomy.
In 1582, Pope Gregory XIII redid the calendar, because it had become obvious that Julius Caesar’s figure of exactly 365.25 days per year was a little too much. Ten days in October were skipped to bring the Equinox back to the day that it had fallen on at the time of the Council of Nicea in 325, when the rules for Easter were first officially set. At the same time, the rules for the hypothetical moon were completely rewritten. This is, of course, the Gregorian Calendar.
For a long time, Protestants refused to have anything to do with it out of spite, but, after about 200 years, the Church of England decided that, no matter how evil they thought the Pope was, the astronomical facts were plain. However, to avoid copying Rome, instead of using Gregory’s new hypothetical moon, they made some patches to the old one. This is the “New Style” calendar, and, in September of 1752, eleven days were skipped. At present, the Gregorian Calendar and the New Style Calendar give the same results, but they will not always.
In the 20th century, some reform-minded Eastern Orthodox decided to tackle the problem, and came up with yet another calendar, the “Revised Julian”, which by then involved skipping thirteen days. Like the New Style Calendar, it is in sync with the Gregorian Calendar now, but will not always be. On the whole, and for whatever it’s worth, the Revised Julian is the most astronomically accurate.