Hi fscmidt, I watched the video on the Eastern Orthodox Church, and it was very informative. I don't know much about the Eastern Orthodox. It is true, however, that they can trace their origin back to the apostles in the Bible, like the Catholic Church. There was only one church back then, 2,000 years ago. Peter, Paul and the other apostles went to Rome and Greece to spread the new Christian faith. That is recorded in the Bible as in Paul's letters to the Romans and his letters to the Corinthians. So what they are saying about their origin is true.
In the early years the church was ruled by patriarchs. Each geographical location had their own patriarch. In 1054 AD, the great schism took place, which divided the east from the west.
In the east they have patriarchs over different region. In the west, Roman Catholicism is headed by the Pope. The structure is hierarchical, with the Pope, then cardinals, archbishops, bishops, priest, etc.
The Roman Catholic Church is different from the Eastern Orthodox because it claims it's apostolic succession from the chief of the apostles, Peter, using the biblical quote, Matthew 16:18: "Thou art Peter and upon this rock I build my church."
http:///www.catholicbible101.com/thouartpeter.htm
Peter went to Rome as head of the apostles and establish the faith. He died in Rome. And upon his burial site, St. Peter's Church, the Vatican, was officially built.
And unlike the eastern Orthodox Church, Catholicism has fulfilled Christ's command to go ye into all the world and and spread the message. Mark 16:15. So you'll find Catholicism in every country. The word "Catholic", itself means "universal."
Many protestant religions, in their prayer the "Apostle's Creed," say "I believe in the "catholic" church" to signify the authenticity of their own particular beliefs, for the apostles creed is the gold standard of who is Christian and who is not.
I hope this helps.