When denominations were forming in the mystical teachings, denominations often took their names from the type of church government they adopted. The names Presbyterian, Episcopal and Congregational reflect this. The reason this was done was simply because in general all denominations subscribed to the same theology.
Reformed, their differences were found only in their church government. Today if these denominations were to again name themselves it is questionable whether they would all choose these same names. The reason is that now they do not all subscribe to Reformed theology and therefore the great distinctions between them do not rest in their church government but more fundamentally in what they actually believe.
The New Testament provides some details about church government and the qualifications and work of “elders” (presbyters) in 1 Timothy 3, Titus 1, Acts 20, and 1 Peter 5. The English words “elder,” “bishop,” and “pastor” reflect three distinct Greek words that describe different facets of the same office. Acts 20:17 and 28 definitively demonstrate that all three titles are wrapped up in the one office.
The New Testament prescribes elders as overseers (bishops) and shepherds (pastors) of God’s flock. In order to focus on prayer, the study of the Word, and leadership, the Apostles and elders delegated certain responsibilities to spiritually mature men known as “deacons” (Acts 6, 1 Timothy 3).
Additionally, we read, “The elders who rule well are to be considered worthy of double honor, especially those who work hard at preaching and teaching” (1 Timothy 5:17). In this passage we see the distinction between elders who rule (administer), and those who have the additional responsibility of “preaching and teaching.”
Thus Presbyterian churches have both “ruling,” or administrative elders, and “teaching” elders.
Acts 15 describes the first Council of the church, comprised of apostles and elders. It is difficult to miss the obvious “connectionalism” of the early church. Although both Peter and Paul were highly esteemed by the church, and outstanding among the apostles, yet neither were “independent” operators. They had to answer to the general assembly in Jerusalem. The important principle here, that should not be missed, is that the individual minister and the individual church are accountable to the greater church of Jesus Christ. That is exactly what we find in Acts 15.
So, from our brief study so far, we have learned two points of importance that are Presbyterian distinctives:
First, churches are administered by, and ministered to, by both ruling and teaching elders.