When the Nicene Creed was formulated, in the 4th century, there was simply the One, Holy, Catholic, and Apostolic Church of Christ, which included Rome, Alexandria (Copts), Constantinople (Greeks/Byzantines), Antioch (Syriacs), etc… unfortunately, due to Christological disagreements at the Council of Chalcedon (held in the year 451), the Churches of Alexandria and Antioch (the spiritual ancestors of the modern Coptic and Syriac Orthodox Churches) severed communion with Rome (Latins - the spiritual ancestors of todays Latin or Roman Catholics) and Constantinople (the spiritual ancestors of todays Eastern/Byzantine Orthodox and Catholics). Constantinople, and the local churches in communion with her, and Rome broke communion many centuries later in the 11th century (though it was a gradual process). As a result of these sad divisions, there are three primary bodies that were once part of the ancient One, Holy, Catholic, and Apostolic Church of the Nicene Creed:
-The Catholic Church (all of those churches that are in communion with Rome)
-The Eastern Orthodox Churches (those churches who practice the Byzantine Rite in communion with Constantinople)
-The Oriental Orthodox Churches (Copts, Syriacs, Armenians, etc - those churches who rejected the Council of Chalcedon in 451).
Some members of these various Eastern and Oriental Churches, in later centuries, reconciled with Rome and became the Eastern and Oriental Catholic Churches. These Churches seek to hold on to the venerable traditions of their brothers and sisters in the Eastern and Oriental Orthodox Churches while fully belonging to the Catholic Church in communion with the Pope in Rome.
It is important to note that from a Catholic perspective, the Eastern and Oriental Orthodox Churches do have valid sacraments (unlike Protestants) - their eucharist is a true eucharist and their priests are true priests. For this reason, the Catechism states that the Orthodox Churches are in an imperfect communion with the Catholic Church. Unfortunately, we are not free to receive holy communion in these churches until full communion is reestablished. The fact that they celebrate valid sacraments, which by definition must flow through the Church, Christ’s body on earth, demonstrates that they are in some sense united to the Catholic Church - but only imperfectly so - their lack of full communion with the bishop of Rome, from a Catholic perspective, is a defect. From a Catholic perspective, the One, Holy, Catholic, and Apostolic Church is comprised of those churches in communion with the successor of St. Peter - the Bishop of Rome. The various Orthodox Churches disagree.