So very much of the following I learned from Dr. Douglas E. Brown, Jr., whose teaching at Harding University Graduate School of Religion has had a sizable impact on the theological thought of preachers and professors among the Churches of Christ.
To make my work here more readable, I've placed documentation in numbered footnotes. Comments, corrections, questions, and disagreements are welcome.
In the previous post, I described some of the effects that the 1925 "Scopes Monkey Trial" had on conservative Protestantism in the United States. In short, over the next two decades those American Christians called "Fundamentalists" reacted in different ways and soon formed three distinctive groups which can described as follows:
1. Closed Fundamentalism -- defiant, militant, insular (e.g., Bob Jones University, and Carl McIntire's "American Council of Christian Churches").
2. Open Fundamentalism -- still mostly separate from the broader culture, but more-accomodating on some points than the group described as "Closed" (e.g., Moody Bible Instititute).
3. Evangelicalism -- determined to be culturally-engaged and world-class, and to avoid anti-intellectualism (e.g., National Association of Evangelicals).
Because the word "evangelical" was hardly new, the third and most-progressive group often referred to itself as “Neo-evangelicalism.” This group differentiated itself from both of the others in at least four ways:
First, evangelicals disassociated themselves from fundamentalist forms of separatism. Evangelicals did not abandon separation as a mark of Christian identity. But they did reject what they saw as fundamentalist extremes and a failure to promote cross-denominational unity and cooperation. An example of this point, E. J. Carnell identified fundamentalism as "the quest for negative status, the elevation of minor issues to a place of major importance, the use of social morays as a norm of virtue, the toleration of one’s own prejudices but not the prejudices of others, the confusion of the church with a denomination, and the avoidance of prophetic scrutiny by using the word of God as an instrument of self security but not self criticism.” 
Second, evangelicals disassociated themselves from the anti-intellectual tendency of the fundamentalists. Here the 1959 statements of evangelical spokesman John Gerstner are typical. The current scene, he said, is characterized by one kind of conservatism that is in “greater conversation with non-evangelical viewpoints.” In spite of the fact that the evangelical tradition “has known some in its fellowship to be obscurantist in their outlook," the best of the evangelicals have always been willing “to discuss vital issues with dispassionate academic objectivity."  Likewise, in 1960 Harold J. Ockenga (pictured here) distinguished evangelicalism from fundamentalism by saying that they were different “in areas of intellectual and ecclesiastical attitude.” 
Third, evangelicals disassociated themselves from the fundamentalist retreat from apologetic interaction with contemporary culture. The early works of Carnell are best examples of this emphasis.  It is likely that other American scholars would have written even more books on Christian apologetics had it not been for the tremendous success of the atheist-turned-Anglican C. S. Lewis. Books by Lewis such as Broadcast Talks, Christian Behaviour, Beyond Personality,  and Miracles  filled much of what was considered a void.
Fourth, evangelicals disassociated themselves from what they perceived to be the weak social concern of fundamentalists. Prior to the early twentieth century, many of those aligned with Protestant orthodoxy had promoted social action as one expression of their faith.  But at least two factors had contributed to a fundamentalist retreat from those historic commitments. In certain pockets of fundamentalism, the movement’s identity was closely connected with dispensational premillennialism. This triggered a heightened expectation of the end time and a pessimistic retreat from general society.  Also, the well-known “social gospel” was clearly associated with liberal theology. Evangelical reaction against fundamentalist disengagement clearly began with the 1947 publication of Carl Henry’s little book The Uneasy Conscience of Modern Fundamentalism.  An early issue of Christianity Today carries on this emphasis by pledging “to apply the biblical revelation vigorously to the contemporary social crisis, by presenting the implications of the total Gospel message in every area of life.” The writer adds, “Fundamentalism has often failed to do this.” 
As concrete expressions of their distance from fundamentalism, evangelicals also established two historic institutions. First, they began a school that would train pastors and other sorts of leaders who would be capable of guiding churches, and who would be qualified to work in the world’s centers of influence: Fuller Theological Seminary was founded in Pasadena, California in May 1947. During the 1930s and 1940s, Charles E. Fuller hosted the immensely popular syndicated radio program, “The Old Fashioned Revival Hour.” At the formation of the Seminary named for his wealthy father, he was joined by Ockenga, pastor of the Park Street Congregational Church in Boston. These were days of bright beginnings. The Seminary was designed by Fuller to become “what Cal Tech is to engineering and West Point to military science.”  Fuller strongly recruited the best scholars among former fundamentalists, not the least of whom was E. J. Carnell. With earned doctorates from Harvard and Boston Universities, Carnell proved to be a powerful influence within the new school and its constituency. Fuller also secured the services of New Testament scholar George Eldon Ladd, whose writings deeply influenced Evangelicals. Significantly, among the faculty at Fuller were converts who had entered evangelical Christianity from mostly-unchurched backgrounds. The best-known and most prolific of these leaders was Carl F. H. Henry. 
Evangelicals also began a representative magazine, a flagship publication designed to express and guide evangelical thought. In 1956, Carl Henry became the founding editor of the magazine which has ever since served as a guide and clearinghouse for contemporary evangelicalism. They named it Christianity Today.
 E. J. Carnell, The Case for Biblical Christianity (Grand Rapids, MI: Eerdmans, 1969), 169-70. Along the same line, Clyde S. Kilby observed a greater tendency “for orthodox believers to wish to get together rather than separate from each other. Those who seem determined to be a law unto themselves are finding it harder to survive at all.” Christianity Today, III (December 22, 1958), 20.
 CT, III (February 16, 1959), 39. See also, III (March 30, 1959), 3.
 CT, V (October 10, 1960), 12.
 Carnell’s first book was An Introduction to Christian Apologetics (Grand Rapids, MI: Eerdmans, 1948). Though his subsequent works were not so directly focused, they frequently took up apologetic themes.
 These three books were published from London by Geoffrey Bles in successive years 1942-44. A decade later, a revised and amplified collection of all three was published as Mere Christianity (London: Geoffrey Bles, 1952).
 London: Geoffrey Bles, 1947.
 See, for example, Clifford S. Griffin, "Religious Benevolence as Social Control, 1815-1860," Mississippi Valley Historical Review, 44 (December 1957): 423-44; Griffin, Their Brothers' Keepers: Moral Stewardship in the United States, 1800-1865, (New Brunswick, NJ: Rutgers University Press, 1960); and Charles I. Foster, An Errand of Mercy: The Evangelical United Front, 1790-1837 (Chapel Hill: University of North Carolina Press, 1960).
 “As evangelical thought developed along a premillennial line (notably since the Niagara Prophetic Conferences, 1868, and thereafter, reaching a certain peak around 1925), it often became increasingly apathetic towards civic involvement, expecting an immediate Second Advent.” George H. Williams and Rodney L. Petersen, “Evangelicals: Society, the State the Nation (1925-75),” in The Evangelicals, rev. ed., D. F. Wells and J. Woodbridge, eds. (Grand Rapids, MI: Baker Book House 1977), 260.
 Grand Rapids, MI: Eerdmans, 1947.
 CT, III (October 13, 1958), 20. The essay is a “Statement of Policy and Purpose” which I presume was written by Carl Henry. As the first editor of CT, Henry continued his focus on this theme. In a substantial essay, “Perspective for Social Action,” he laments the opportunity that had been forfeited by orthodox Protestantism: “Perhaps at no time in modern history was American Protestantism so propitiously situated as at the early twentieth century for a world impact. . . . Sad to say, Protestantism dissipated this great opportunity and certain dire consequences followed hard upon its growing deference to the social gospel. . . . In its reaction against the social gospel, the fundamentalist movement became socially indifferent and even made the inevitability of social decline a part of its credo. To some extent, pessimism resulted from dispensational views which taught that world-wide spiritual apostasy must precede the second coming of Jesus Christ” CT, III (January 9, 1959), 10-11. Likewise, according to a history of neo-evangelicalism’s first 25 years in America, an evangelical “believes that a defense of the Gospel can be coupled with Christian charity and intellectual integrity.” The quote is taken from Ronald Nash’s review of Bruce Shelley, Evangelicalism in America (Grand Rapids, MI: Eerdmans, 1967), in CT, XI (July 7, 1967), 26.
 CT, III (January 19, 1959), 13.
 In addition to the general article by T. P. Weber, “Fuller Theological Seminary,” in Dictionary of Christianity in America, 460-61, a solid book-length treatment is provided by George M. Marsden, Reforming Fundamentalism: Fuller Seminary and the New Evangelicalism (Grand Rapids, MI: Eerdmans, 1987).