You have your wording incorrect. There is Eastern Orthodox, and Eastern Catholic. Both are different Churches.
Eastern Orthodox: The Eastern Orthodox Church was once one Church along with the Roman Catholic Church until the Great Schism in 1054. After 1054, they have been two separate Churches. The difference easiest to recognize is their view of the Bishop of Rome (the Pope). The Roman Catholic Church believes that the Bishop of Rome has the final say in defining doctrine whereas the Eastern Orthodox Church believes Church doctrine can only change when it has been decided in an Ecumenical Council such as the seven that were held before the churches split.
Eastern Catholic: The Eastern Catholic Churches are former Eastern Orthodox Churches that have enter back into communion with the Holy See. They still practice using Eastern Rites, however. (Ex. Married men can be ordained Priests, the Nicene Creed is read without the Filioque clause, etc.)
Hope I answered your question.
~God Bless
Eastern Orthodoxy is just as old as Catholicism. Before 1054 there was simply the Church. No separate denominations or anything. Afterwards, the Catholic and Orthodox churches were formed and later differences in tradition and theology arose. For example, the Catholic Pope is infallible, the Orthodox use a different calendar to calculate Easter, and the Orthodox still use tradition Byzantine style when painting their icons. There are many differences and yet both churches hope to reunite someday to restore the Christian faith to it's once universal state.
the Eastern Orthodox Church and the Roman Catholic Church
Eastern Orthodox
Anyone other than Eastern Orthodox eg Oriental Orthodox, Catholic, Protestant
Roman Catholic, Eastern Orthodox, and Protestant.
Roman Catholic, Protestant, Eastern Orthodox
The Eastern Orthodox religions
Eastern Orthodox Christianity, Christianity, and Catholic.
There are Eastern or Byzantine Rite Catholics but they are in full union with Rome as opposed to the Eastern Orthodox Churches which are not. There was a brief period in the 20th century, when a separate Orthodox Church broke away from the Eastern Orthodox Church in America and formed the America Orthodox Catholic Church. But it was yet another splinter of an already splintered Church. orthodox (small "O") means right belief, and thus is synonymous with Catholic. Now, there is also an Orthodox Catholic Church of America, also not in Communion with the Catholic Church. . You may read about the American Orthodox Catholic Church at the links below.
The catholic church is sometimes considered the collection of churches that developed out of the Great Schism (namely, the Roman Catholic Church and the Eastern Orthodox Church). Although I have never heard someone use the term "catholic orthodox church," I would consider it to be referring to the Eastern Orthodox Christian religion.
No, the Pope is the head of the Roman Catholic church. The Ecumenical Patriarch is the head of the Eastern Orthodox Church.
The Orthodox Churches and the Catholic Church were once united. The Orthodox Churches separated from the Catholic Church over political and doctrinal differences.
Catholic.