In America, the Restoration movement is normally linked with the Stone-Campbell movement. Consisting of a merger between the followers of Barton Stone and of Alexander Campbell, the Stone-Campbell movement with its biblicism strove to remove all forms of accretions not found in Scripture, and go back to, restore, the New Testament church. Subsequently of course, other restorationist groups sprang up, all claiming to restore the Church back to its New Testament "glory" days. Probably the one with the greatest following today is Pentecostalism and its step-daughter the Charismatic movement. Both movements claim to restore all the gifts of the Spirit back to the Church. How Pentecostals and Charismatics interpret church history of course varies, yet regardless of how one strains to find precedents throughout church history, it cannot be denied that before the Azusa Street revival, at least most of the professing church did not hold to the continuing validity of the sign-gifts.
The restoration principle is best defined by Richard T. Hughes as “a reversion undercutting both Catholic and Anglican appeals to a continuity of tradition, to the first, or primitive, order of things narrated in the Protestant Scriptures" [Richard T. Hughes, "Introduction," in Richard T. Hughes, ed., The American Quest for the Primitive Church (Urbana and Chicago, IL: University of Illinois Press, 1988), 2]. How does that compare however to the Reformation principle of Ad Fontes, going back to the sources? The two certainly seem very similar to its appeal to the Scriptures and the New Testament Church. Its similarity can be seen in the fact that in that same book edited by Richard T. Hughes, Thomas H. Olbricht claimed that the New England Puritans were engaging in primitivist/ restorationist thinking (the two terms are not differentiated in the book). But are the two the same? No they are not. The Restorationist principle is largely ahistorical. It ignores history, and skip over history since what matters is to return back to the "pristine New Testament church." The Reformation principle of ad fontes however goes back to the historic Christian Church through interaction and engaging with others, acknowledging the fact of time and history and our distance from the original events. We can never go back to the New Testament Church, for we cannot go back in time. As Mark Noll makes plain the distinction between primitivist Christianity and historic Christianity, in historic Christianity "the Bible was a book to be studied with the history of the church, not against it" [Mark Noll, "Primitivism in Fundamentalism and American Biblical Scholarship," in Ibid., 125].
The issue of history divides the Reformed tradition from any and all restorationists. We affirm history and the need to wrestle with history. Restoratinists minimize history, even if they may not outrightly deny it. History to them is not to be regarded as real temporal progression but rather a mere passing of time which leaves concepts and ideas and everything else more or less intact. That is why Pentecostals and Charismatics think that the mere repetition of 1 Cor. 14:39 is sufficient to deal with the topic of whether the sign-gifts have ceased. There is a strong strain of the denial of the historical situatedness of the Word of God in its current ectypal expression, making the Bible into a Systematics textbook instead of the ectypal expression of God's Word that is situated in history.
The Reformation principle and the Restorationist principles therefore are not the same. Historical development has proven that history does play a key role in theologizing. In other words, everyone has traditions. The Stone-Campbell restorationist movement is radically different from the "restoration" by Joseph Smith, which is different from the restorationist movements of the Seventh-Day Baptists and Adventists, and all of them are different from the restorationist movement known as Pentecostalism. As Henry Warden Bowden, after surveying all these various restorationist movements, claimed, "'the restoration ideal' is truly a protean concept" [Henry Warden Bowden, "Perplexity over a Protean Principle," in Ibid., 176]. All the various restorationist movements have proven that it is impossible to situate oneself outside of time and history, and thus "restoration" is a mirage. It is a myth that one can go back to the New Testament Church, and thus Restoration itself is not only errant but absolutely impossible.