This is a good breakdown of the reasons for the differences: What’s the Difference Between Easter and Orthodox Easter?

Long story short, Easter is found by calculating the first Sunday after the first full moon falling on or after the vernal equinox. The Western church (Catholics and Protestants) use the modern Gregorian calendar to find this date, whereas the Eastern church (Orthodox) use the old Julian calendar, ensuring that Easter (we call it Pascha) falls after the Jewish celebration of Passover.

Some Orthodox traditions, primarily the Russian Orthodox, use the Julian calendar for the Nativity as well, and celebrate Christmas on January 7.

The wikipedia article for "Easter" covers the bases pretty well.

TL;DR- The date of Easter is determined based on a lunisolar calendar, similar to the Hebrew calendar, so it falls on a different date every year, similarly to how Jewish holidays fall on different dates.

The rule is it falls on the Sunday on or after the full moon that occurs on or after the spring equinox (although not the actual solar equinox, because it was decided a long time ago that for church purposes they would use March 21 as the equinox date)

That was decided with the council of Nicea in 325, before the schism between eastern and western churches, so pretty much the whole Christian world was on the same page at the time. When they split 1054, they still stayed on the same page, because they were both still using the Julian calendar, but that March 21st date slowly drifted further and further away from the actual equinox because they didn't account for leap years properly.

Then in 1524, The Catholic Church decided to do something about that, and came out with the Gregorian calendar. Catholics made the switch pretty much immediately, and most protestant Churches did too over the next couple of hundred years, so they're all pretty much on the same page

Most of the eastern orthodox churches, however, still base their holidays off of the Julian calendar, even though for pretty much everything else people use the Gregorian calendar, and the two calendars are currently 13 days off, so March 21st in the Julian calendar is April 3rd on the Gregorian calendar (and in 2100 after the Julian calendar has a leap year that the Gregorian doesn't, it'll increase to 14 days difference)

So depending on how the full moons line up, there can be a pretty significant difference in when Easter falls for the two churches. Next year they will actually fall on the same date, which will happen occasionally until the year 2700 when the two calendars will have drifted too far apart for it to ever happen again (or at least until they get so far out of sync that they're almost a full year behind, I'm too lazy to do the math but we're talking like tens or hundreds of thousands of years in the future when that happens, so hardly even worth worrying about right now)

Similarly, most Orthodox churches celebrate Christmas on January 7th currently, because it's 13 days after December 25th on the Gregorian calendar. It's still December 25th on the Julian calendar though. And after 2100 it will be on January 8th (unless they adopt the Gregorian calendar before then, or like most Ukrainian orthodox churches decided to do last year, decide to just celebrate it on December 25th with most of the rest of the world)