Greek Easter—more accurately called Orthodox Easter or Pascha—is the celebration of Christ's resurrection as observed by the Greek Orthodox Church and other Eastern Orthodox churches, while "regular" Easter usually refers to the date observed by Western Christian traditions (Catholic, Protestant, Anglican, etc.). The core theological event being celebrated is identical, but the dates often differ, and there are some distinct traditions.
Why the dates differ: Both Easters are calculated using the same basic rule established at the Council of Nicaea in 325 AD — Easter falls on the first Sunday after the first full moon following the spring equinox. However, they use different calendars to calculate this. Western churches use the Gregorian calendar (the standard civil calendar most of the world uses today). Orthodox churches use the older Julian calendar to determine the ecclesiastical full moon and equinox dates, even though many Orthodox countries use the Gregorian calendar for everyday life. The Julian calendar has drifted about 13 days behind the Gregorian calendar over the centuries, which shifts the calculation.
Additionally, Orthodox tradition requires that Easter fall after Jewish Passover, in keeping with the biblical timeline of the events. Western Easter does not have this requirement, so occasionally Western Easter falls before Passover.
As a result, Orthodox and Western Easter can fall on the same date (roughly once every few years) or be separated by one to five weeks.
Other differences: Greek/Orthodox Easter involves distinct customs, such as a midnight Resurrection service, cracking red-dyed eggs (symbolizing the resurrection and Christ's blood), a Lenten fast that is generally longer and stricter than in Western tradition, breaking the fast with lamb-based meals like magiritsa soup, and greeting others with "Christos Anesti" ("Christ is Risen").
Despite these differences, both observances commemorate the same event; they simply follow different calendrical calculations and cultural customs rooted in their respective church traditions.