I would like to know the differences between what the Presbyterians believe and what Lutherans believe.
Just as all churches that bear the name “Lutheran” do not teach the same as other “Lutherans,” so not all churches that bear the name “Presbyterian” teach exactly the same. We can, however, speak of what Presbyterians believed historically and compare it with what confessional Lutherans believe.
Historically, as strict Calvinists, Presbyterians taught that from eternity God elected some to be saved and some to be damned (double predestination). By no means do all Presbyterians believe this today. Confessional Lutherans believe that from eternity God chose those whom he would convert through the gospel and preserve in faith to eternal life. See Ephesians 1:4-6; Romans 8:29,30). Confessional Lutherans reject the notion that unbelievers were predestined to damnation, for “God does not will that any should perish” (see 1 Timothy 2:4 and 2 Peter 3:9).
Historically, and as a corollary of the Calvinist belief in double predestination, Presbyterians taught that Christ atoned for the sins only of those predestined for life in heaven. Confessional Lutherans believe that Jesus Christ, the God-man, was sent by the Father to atone for the sins of all people, and that he did so. See Romans 5:18,19; Isaiah 53:6; 2 Corinthians 5:19; and John 1:29.
Historically, Presbyterians believed that it is impossible for a believer to fall from the faith. Confessional Lutherans believe that it is possible for believers to fall from faith. See 1 Corinthians 10:12.
Historically, Presbyterians have believed that Sunday has replaced Saturday as the Sabbath, to be observed in a way similar to the Old Testament regulations. Confessional Lutherans believe that New Testament believers are free to gather for worship on Sunday (or any other day), without special rules regarding work or recreation. See Colossians 2:16,17: “Do not let anyone judge you . . . with regard to a Sabbath day. These are a shadow of the things that were to come; the reality, however, is found in Christ.”
The name “Presbyterian” means “having elders (teaching and ruling or presiding),” as the only form of church government that has God’s approval. Confessional Lutherans believe that the Lord has instituted and provides for the gospel ministry, but that there are no commands in the New Testament as to forms of organization.
Like other Protestant (non-Lutheran) churches, Presbyterians do not believe that Baptism and the Lord’s Supper are means of grace—forms of the gospel through which the Holy Spirit gives and strengthens faith. Confessional Lutherans believe that Baptism gives new life (Titus 3:5) and cleanses from all sin (Acts 2:38). Confessional Lutherans believe that as believers receive Christ’s body and blood under the bread and wine they also receive the forgiveness of sins (Matthew 26:28; 1 Corinthians 10:16).Presbyterians do not believe communicants receive the Lord’s Body and Blood in his Supper.