This is a much too long brief discourse on ecclesiology that might help with your questions. Or not.
A church is a group of people gathered in the Lord’s name to worship and pray. Wherever 2 or more are gathered, the Lord is in their midst. Churches are united with each other through their union with Christ and by their sharing some common characteristics.
Once you begin bringing people and churches together, institutional frameworks facilitate commonalities. The churches in a specific area are called Particular churches, and reflect the institutional role of the bishop that brings them together.
All churches, united in Christ, form the One Holy Catholic Church. The Papacy gives an institutional element that brings these people together, rooted in the apostolic dimension of the One Church.
While most christians believe in the One Church mentiined in the creed, Catholics are the only ones who identify their united churches as the One Church. Our institutions are meant to serve the union of all christians with Christ, a somewhat larger mission than others claim.
The Orthodox are organized at a level above the Particular churches, with the Patriarch uniting a larger grouping with a national identity. These are seen as being part of the One Church for a nation/ethnic group. The Ecumenical Patriarch in Istanbul is not seen as an institution for the One Church, but as “first among equals” among all the Patriarchs.
Anglicans do not see the collection of their Particular churches as the One Church either. Together, they are, and are called, the Anglican Communion of Churches.