Greeting the Churches

I must admit that most times I read quickly through the greetings at the beginnings of the epistles, nearly skipping over them to get to the next part. This time (I've been reading Corinthians) I got stuck on the greeting. It suddenly seemed very significant, especially in how we think of churches as relating to The Church. Paul addressed the Corinthian churches this way in the first letter; "To the church of God which is at Corinth, to those who are sanctified in Christ Jesus, called to be saints, with all who in every place call on the name of Jesus Christ our Lord, both theirs and ours" and this way in the second letter; "To the church of God which is at Corinth, with all the saints who are in all Achaia".

To the church of God which is at Corinth...
My NKJV has this note about it: "A local church of God is a group of people who identify themselves with God and gather together to worship and serve Him". That's the exact opposite of what understanding hit me when I read the greeting. Rather, I read it to mean that Paul was addressing The Church of God which was in Corinth, the fullness of the Church which was in the church. Instead of greeting "people who identify themselves with God", Paul's greeting makes clear that he is writing to people whom Christ has gathered into His Body. That's a significant difference.