I know I belonged to both. And BTW, the ICofC do have different names rather than by city. Both the mainline CofC and the ICofC believe they are God's sole remnant on earth.
For Florida, at least, that's how they call themselves. The South Florida Church sells and uses "non-remnant" books, music and materials. For example, books by Joshua Harris. I wonder why they would do that if they believe outsiders aren't true Christians.
The COC does not believe it is the sole remnant of anything. We believe we are following God's instruction on what to do for salvation. Now, if we follow God's instruction for salvation, doesn't that mean we are in His church?
Do others have to follow God's instruction or do they just get to determine what they believe?
We would then have millions of ways to get salvation. But, we have one God giving that salvation. I would think it would behoove us to find out what God says is needed for salvation. If you go to the bible to find out and follow the instructions, you too will become a member of the church of Christ. Christ is the head of the church, and when you follow the bible instructions on believing and salvation, (not man's determined creed, not a separate instruction book) you too will be a Christian and a member of Christ's church as spelled out in the Bible.
Does that explain where you get we are saying we are the sole remnant or something? Of course we say we are members of Christ's church because we are. Of course we feel that this is what God intended because we intend to do what God intended and went to the Bible to find out.
Now can you say the same of denominations or churches that have come up with their own version of what is correct? Are they following what is spelled out in the Bible or what they determined the people should believe?
I have been a member of the church of Christ for 35 years, and my family has been a part of the church for at least 5 generations. I have never heard anybody use those terms! There are people all over the world that follow God's word. They may or may not have a sign nailed on the wall where they worship that says "Church of Christ, but they are Christians according to God's commands.
Old Testament history and prophecy is complicated, and I have not studied it enough in recent years, but the only remnant I've ever seen discussed in the Bible is the remnant of Israel. Could I be a part of that remnant if I'm not Jewish?