I think this website agrees with your views
but it clarifies better the dual use of the words:
http://theoslog.com/definitionofassembly.html
The New Testament uses the word
ekklhsia in a number of ways:
1. A general assembly of people. - Israel in the wilderness was called “the
ekklhsia in the wilderness” (Acts 7:38). The confused and angry mob (
ekklhsia) that was rioting against Paul in Ephesus was encouraged to take their case to a lawful assembly (
ekklhsia) (Acts 19:32, 39, 41). A religious gathering (Heb. 2:12; cf. Ps. 22:22).
2. A gathering of Christians. Frequently the New Testament speaks of the
ekklhsia which was in some particular location: “the
ekklhsia which was at Jerusalem” (Acts 8:1); “the
ekklhsia which was at Antioch” (Acts 13:1); “the
ekklhsia of God which is at Corinth” (I Cor. 1:2).
Ekklhsia is also used in the plural for a group of local churches (I Cor. 16:19; Gal. 1:2).
3. All professing Believers. In this sense
ekklhsia takes on a meaning almost synonymous all with Christians. Paul said to the Romans, “the
ekklhsiai (plural) of Christ salute you” (Rom. 16:16). To the Galatians Paul wrote that he had “persecuted the
ekklhsia of God” (Gal. 13:13). In these statements no particular local assembly is in view. Paul is speaking of Christians everywhere.
4. The Universal body of Christ. The word
ekklhsia can refer, not only to a local gathering of Christians, but also to the general body of Christ. This includes all Believers who have placed their faith in Christ whether they are living or dead. Paul identified the
ekklhsia as Christ’s body in his letters to the Ephesians and to the Colossians (Eph. 1:22-23; Col. 1:18). All Believers in this dispensation are united with each other and with Christ. Christ is head of the body and Lord of the
ekklhsia.
Lightner writes regarding the Universal
Ekklhsia:
There are a number of usages of
ekklhsia that do not seem to refer to a local assembly of believers. Instead, they speak of that company of believers formed on the day of Pentecost into the body of Christ, which has been growing ever since as sinners trust Christ alone as Savior and are added to it. This company of the redeemed is called the church without consideration of whether or not those who are part of it are members of local churches.
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