The Church of Christ is first and foremost an eternal, divine and human organism - the Body of Christ, a unity of many that transcends space and time. The Church of Christ, like the Eucharist (which is also the Body of Christ), is manifested by the Holy Spirit in space and time. It intersects with our reality and is revealed in the catholic Church. The catholic Church, the “whole Church,” is the local Eucharistic assembly, presided over by its bishop who is the icon of the Father, steward of Christ, and as St. Peter, primate of the assembly and symbol of unity. This simultaneous manifestation of the catholic Church in many places at the same time calls for a manifestation of identity and communion between all the catholic Churches. This so-called “universal Church” (or “Catholic Church” or “common union”), inasmuch as the political realities of our world permit its manifestation, should express the unity of the common union of Churches. This unity is made possible by the existence of a worldwide primate as visible symbol of unity, not unlike to bishop of the (local) catholic Church, but functionally, not ontologically.
The local Church centered on the bishop is “the catholic Church” and indeed the full manifestation of the Body of Christ.
If the local Church (the “diocese”) is “the Catholic Church”, it contains in itself the fullness of means of grace, sanctification and salvation, whether or not “united” into a particular geopolitical superstructure. In other words, Cyprian of Carthage, Stephen of Rome and Firmilian of Caesarea can still be bishops of the catholic Church and saints in spite of their ruptures of communion. The Churches of St. Thomas in India, or those of Ethiopia were always one, holy, catholic and apostolic even when disconnected from Rome or Constantinople. It also means that the saints (of east and West, for instance St. Francis of Assisi and St. Sergius) do not drop in and out of the catholic Church because their patriarchs are quarreling over who knows what. Likewise, the idea that salvation is tied to a particular worldwide organism becomes obsolete.