Church "Of Christ"
The term “church” is a collective noun like “jury,” “army,” and “herd.” The term “jury” collects jurors; the term “army” collects soldiers; and the term “herd” may collect cattle. The term “church” is used to collect Israelites (Acts 7.38; “congregation” (NASB); “assembly” (NIV)), rioters (Acts 19.32; “assembly”), Greek citizens (Acts 19.39; “assembly”), or, when used to refer to a church “of Christ,” to collect saints (1 Corinthians 1.2).
Saints banded together to have fellowship in those duties peculiar to their relationship to God in Christ are referred to as a church “of Christ” (Romans 16.16), church “of God” (1 Corinthians 1.2), or a church “in God the Father and the Lord Jesus Christ” (1 Thessalonians 1.1). These terms were used interchangeably. When Paul wrote, “the churches of Christ salute you” (Romans 16.16), he was in Corinth (thus Corinth included in “churches of Christ”), but when he wrote to Corinth, he wrote, “to the church of God” (1 Corinthians 1.2). Aristarchus and Secundus of the Thessalonians were with Paul when he wrote this greeting from “the churches of Christ” (Acts 20.2-4), but when he wrote to Thessalonica, he addressed them as “the church of the Thessalonians in God the Father and the Lord Jesus Christ” (1 Thessalonians 1.1).
Now, while the “church of Christ” collects saints, not every collection of saints is a church of Christ. You may have a collection of people who happen to be saints engaged in a business (i.e., a rest home), teaching secular education (i.e., a college), or having fun (i.e., a picnic). None of these constitute a “church of Christ.” Saints banded together scripturally to do the work “of Christ” (Philippians 2.30; 1.27). constitute a “church of Christ.” Thus, we find the “church of Christ” in Philippi banded together to have fellowship with Paul in preaching the gospel of Christ (Philippians 1.1-5; 2.30; 4.15). Likewise, we find the church “in God the Father and the Lord Jesus Christ” in Ephesus authorized to relieve widows who have no family to relieve them and have “fixed their hope on God” (1 Timothy 1.3; 5.3,5,16). Again, the “church of God” in Corinth worked together to provide relief for the needy saints in Jerusalem (1 Corinthians 1.2; 16.1-3; 2 Corinthians 8-9; Romans 15.25-26). The “church of Christ” in Colossae assembled to sin psalms, hymns, and spiritual songs expressive of the joy and thanksgiving they felt because the "word of Christ” richly dwelt in them (Colossians 3.15-16). Never do we find churches of Christ engaged in anything but the work of Christ — no entertainment, no social activities, no politics, no secular business, no general benevolence.
Just calling the tail on a dog a leg does not make it a dog running on five legs. Neither does simply calling a collective a “church of Christ” mean that it is functioning as such.