You are confusing the Easter Rites of the Roman Catholic Church, with the various Orthodox Churches.
The Eastern Rites of the Roman Catholic Church follow many of the same liturgical practices as the orthodox do. The biggest difference is, they are in full union with the Church of Rome (also called the Latin Rite) and they acknowledge the supremacy of the Pope.
The Orthodox Churches do NOT recognize the supremacy of the Pope. They consider him to be “First among Equals”, believing that every Bishop has the same authority and the same leadership rights as any other Bishop. Therefore, the Bishop of Rome, while his opinions should be listened to, has no more authority than any other Bishop.
They also reject the wording of the Western version of the Nicean Creed, and many other liturgical practices and beliefs of the Roman Church. They do not accept the concept of infallibility of the Pope, as just one of many examples There are some very profound differences between those religions, and their Eastern Catholic Cousins.
The Eastern Catholics do accept the Latin Rite’s versions of various theological matters, and they do recognize that the Bishop of Rome has Supremacy over all other Bishops. They also accept the concept of the Infallibility of the Pope in Matters of Faith and Morals.
John Paul II did indeed call, repeatedly, for union among the Eastern Orthodox Churches and the Latin Rite. However, he never attained this, and the two sides are just as far apart as ever.
The only good thing is that both sides have lifted the excommunications of the other.