THE WELS SAY THE DIFFERENCES ARE:
The Wisconsin Synod terminated fellowship with the Lutheran Church-Missouri Synod in 1961 because of differences in the doctrine and practice of church fellowship. Over the years the Missouri Synod had departed from the doctrine and practice of fellowship long held by the members of the Synodical Conference in which the Wisconsin Synod and the Missouri Synod shared confessional fellowship.
The Wisconsin Synod teaches that agreement on all the teachings of Scripture is necessary for all forms of fellowship. The Missouri Synod teaches that full agreement is necessary only for altar and pulpit fellowship. Wisconsin teaches that the same scriptural principles apply to all forms of church or religious fellowship. All joint prayer is an expression of fellowship. Missouri teaches that there can be joint prayer that is not an act of fellowship. In practice Missouri also indicates that full agreement is not necessary for worship at occasional joint Christian celebrations, Reformation services, convocations, rallies. Some Missouri pastors allow "ecumenical wedding services" at which pastors or priests outside their fellowship may participate.
Wisconsin practices "close" or "closed" communion, inviting to our altars only those who are members of congregations in our fellowship. Although Missouri officially teaches "close(d)" communion, many pastors and churches practice "open" communion, allowing joint communion with those not in doctrinal agreement with the Missouri Synod.
There are also differences in the doctrine of the church and ministry between the two synods. Wisconsin teaches that God has not ordained any particular form of the church. The invisible church is present in the local congregation and the synod. Both can be called church in the same sense. Missouri's official teaching seems to be that the local congregation is the only "divinely appointed" form of the church. By contrast the synod is a human arrangement.
Wisconsin teaches that the pastor of a local congregation is only one form of the divinely instituted public ministry. Other forms are teachers, professors, called administrators, etc. The specific form is determined by the church's call. Missouri seems to teach that the only divinely instituted form of the public ministry is that of pastor of a local congregation. All other positions are auxiliary to this. However, there appears to be a number of different teachings on the church and ministry in the Missouri Synod.
Because Scripture assigns the headship role to men and a helping role to women, only men serve in offices and roles that involve an exercise of authority over other men. Missouri does not allow women to serve as pastors but allows women to serve in a number of areas which involve the exercise of authority over men.
A continuing problem in the Missouri Synod seems to be an unwillingness or inability to exercise doctrinal discipline with those who teach and practice contrary to Scripture or the public doctrine of the Missouri Synod.
THE LCMS SAYS THE DIFFERENCES ARE:
1) The biblical understanding of fellowship.
The WELS holds to what is called the "unit concept" of fellowship, which places virtually all joint expressions of the Christian faith on the same level. In an official statement made in 1960 the WELS states, "Church fellowship should therefore be treated as a unit concept, covering every joint expression, manifestation, and demonstration of a common faith" (Doctrinal Statements of the Wisconsin Evangelical Lutheran Synod, 1970, pp. 51-52). The LCMS, however, has historically not understood or practiced church fellowship in this way. Our Synod, for example, has made a distinction between altar and pulpit fellowship (for which full doctrinal agreement is required) and other manifestations of Christian fellowship, such as prayer fellowship (which do not necessarily require full doctrinal agreement). Disagreements on this issue led the Wisconsin to break fellowship with the LCMS in 1961.
2) The doctrine of the ministry. <~ THIS IS BIG
With respect to the doctrine of the ministry, since the days of C. F. W. Walther our Synod has held that the office of the public ministry (the pastoral office) according to the Scriptures is the one divinely established office in the church, while the church possesses the freedom to create other offices, by human institution, from time to time to assist in the carrying out of the functions of the pastoral ministry. The WELS' Theses on Church and Ministry, however, expressly deny that the pastoral ministry is specifically instituted by the Lord in contrast to other forms of public ministry (see Doctrinal Statements, pp. 9-11; cf. the Commission on Theology and Church Relations' 1981 report on The Ministry: Office, Procedures, and Nomenclature.
3) The role of women in the church.
While both the LCMS and the WELS strongly oppose the ordination of women to the pastoral office on Scriptural grounds, the LCMS has concluded that the Scriptures do not forbid woman suffrage in the church. The WELS opposes woman suffrage in the church as contrary to the Scriptures.