Catholicism is under the authority of the Pope, while Orthodoxy is under the authority of its various Patriarchs.
Roman Catholic AnswerThe Catholic Church is the living, breathing, Church founded by Our Blessed Lord before He left this earth. The Eastern Orthodox left the Church in the eleventh century and have pretty much remained unchanged since then. They only accept the early Councils of the Church as infallible, their cultural differences are non-existent, as when the Orthodox broke away from the Church, each Orthodox Church split in two, half remaining with Rome, and half going their own way; so to this day, there is a Greek Uniate Rite, an Armenian Uniate Rite, etc. Uniate rites are full rites within the Catholic Church, which like the Latin Rite, have their own Mass, their own language, and their own way of performing the sacraments. We usually only think of the Latin Rite when we think of the Roman Church but this is incorrect, the Greek Rite is every bit as much the Catholic Church as the Latin Rite is, we in the West are just more familiar with the Latin Rite as it is larger and the Rite that most of us were raised in.the Eastern Orthodox Church and the Roman Catholic Church
No, the Pope is the head of the Roman Catholic church. The Ecumenical Patriarch is the head of the Eastern Orthodox Church.
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.
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.
Roman Catholic AnswerThe Catholic Church is sometimes known as the Western Church to distinguish it from the Eastern Orthodox Church.
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.
Anyone other than Eastern Orthodox eg Oriental Orthodox, Catholic, Protestant
The split between the Eastern Orthodox and the western Catholic Churches was caused by a number of different factors. Namely, neither side could decide on the Pope's role in the church, or the scope of his authority.
That's a long an complicated question. The short answer is the Roman Catholic Church celebrates most holidays on the Western Calendar while the Eastern Orthodox use a slightly different calendar known as the Eastern Calendar. Some years the dates are the same and others they are different. The Roman Catholic Church structure is similar to the Eastern Orthodox. However, the Eastern Orthodox setup a church in each country (generally, America being one notable exception) whereas the Roman Catholics have a world wide structure.
It is when The Roman Catholic Church and The Eastern Orthodox Church had The Great Schism, in which The Roman Catholic Church broke off The Orthodox Church.
The Eastern Orthodox Church uses the Bible. The books in their Canon are slightly different than that of the Roman Catholic, but they also use 3 Maccabees, Psalm 151, and 1 Esdras.