Is the Eastern Orthodox Church part of the Catholic Church?
In my reading, I saw mentions of Eastern-rite Catholics, and in other places, I saw Eastern Orthodox Churches. Are they not the same, and are they part of the Catholic Church?
Eastern-rite Catholics are part of the Catholic Church and are in full communion with the Pope. However, the Eastern Orthodox Church is not part of the Catholic Church. The two major Churches have been separated since 1054. The rift was both theological and political, and both parties made mistakes.
The two parties share a long history and even today share a whole lot in common in faith. However, since the split from the legitimate authority of the Pope, they are no longer Catholics.
There are still ongoing talks to heal old wounds and restore full communion between the Eastern Orthodox churches and the Catholic Church.
The Catholic Church has a number of self-governing Churches in full communion with the Pope. One of those is the Roman Catholic Church or the Latin rite. You can read more about this here. It is a very interesting topic.