To understand the difference between the local church and the universal church, one must get a basic definition of each. The local church is a group of professing believers in Jesus Christ who meet in some particular location on a regular basis. The universal church is made up of all believers in Jesus Christ worldwide. The term church is a translation of a Greek word having to do with a meeting together or an “assembly” (1 Thessalonians 2:14; 2 Thessalonians 1:1). This word pertains to the work of God in saving and sanctifying believers as “called-out ones.” Another Greek word that speaks of ownership and literally means “belonging to the Lord” is transliterated as church, but it is only used twice in the New Testament and never in direct reference to the church (1 Corinthians 11:20; Revelation 1:10).
A local church is normally defined as a local assembly of all who profess faith and allegiance to Christ. Most often, the Greek word ekklesia is used in reference to the local assembly (1 Thessalonians 1:1; 1 Corinthians 4:17; 2 Corinthians 11:8). There is not just one specific local church in any one area, necessarily. There are many local churches in larger cities.
The universal church is the name given to the church worldwide. In this case the idea of the church is not so much the assembly itself but those constituting the church. The church is the church even when it is not holding an official meeting. In Acts 8:3, one can see that the church is still the church even when its members are at home. In Acts 9:31, the King James rendering of the plural word churches should actually be the singular church, which describes the universal church, not just local churches. Sometimes the universal church is called the “invisible church”—invisible in the sense of having no street address, GPS coordinates, or physical building and in the sense that only God can see who is truly saved. Of course, the church is never described in Scripture as “invisible,” and, as a city set on a hill, it is surely meant to be visible (Matthew 5:14). Here are more verses that talk about the universal church: 1 Corinthians 12:28; 15:9; Matthew 16:18; Ephesians 1:22-23; Colossians 1:18.