I have excerpted the most important parts of the essay here for your benefit. I encourage you to read the whole thing, and (if you have some time) to read the previous essays he’s done on this same theme. Note: in the excerpt below, words in brackets and any bolded emphasis are mine.
Fundamentalism surfaced in about 1900 as a doctrinal and ecclesiastical reaction against the influence of theological liberalism… It grew out of an American evangelical coalition that stretched across the denominations, produced the Bible conference movement, built mission agencies and Bible institutes, and produced The Fundamentals. This coalition has come to be known as proto-fundamentalism….
As the battles [against liberal theology] within the denominations warmed up, three evangelical groups became identifiable. One was a militant minority that intended to oust the liberals. These were the fundamentalists. Another was a minority that stood with the liberals, though they themselves were evangelical. These were the indifferentists.
These two groups did not exhaust the spectrum, however. A third group was present. It was a larger group than either the fundamentalists or the indifferentists. This group constituted what Richard Nixon would someday call the “silent majority.”
This silent majority was firmly evangelical and was usually willing to be labeled as fundamentalist. For the most part, the members of this majority agreed with the fundamentalist desire to be rid of the liberals. They were, however, squeamish about some of the tactics employed by fundamentalists. They would have rejoiced if the liberals had simply walked away from the denominations, but as a full-scale ecclesiastical conflict loomed, they lacked the lust for battle….
Institutions like Wheaton and Moody certainly opposed liberalism from a distance, but they did not actually have to fight liberals. They were outside the denominations and de facto removed from fellowship with liberalism. Their focus was on building a positive network of missions, education, publishing, conferences, and itinerancy….
Eventually, the fundamentalists either left their denominations or were forced out. As they built new missions, schools, and denominations, they drew help and support from the interdenominational network. For a time, it looked as if fundamentalism and the silent majority might reconverge into a single, self-aware movement.
The thing that kept that from happening was the emergence of the new evangelicalism. [The attitude of co-belligerence with liberal apostates, which amounted to a rejection of separation — my defiinition].
The whole thing came to a head with Billy Graham’s 1957 crusade in New York City. This was the crusade that solidified a New Evangelical coalition and made Graham its captain. The cooperative evangelism of Billy Graham involved a clear rejection of separation from apostasy. Consequently, it led to a final break between Graham and fundamentalism.
What about the silent majority, the evangelical mainstream, the people who were the most direct heirs of the old proto-fundamentalism? Certainly, they did not approve of Graham’s cooperative evangelism. Unlike fundamentalists, however, they stopped short of breaking with Graham. He was the world’s most successful evangelist, and they felt themselves drawn to him. They had no desire to fellowship with liberals but every desire to support the magnetic young evangelist.
By the early 1960s, neoevangelicals had clearly gained the initiative in missions, evangelism, and scholarship. They welcomed the support of the evangelical mainstream without insisting that other evangelicals break ties with fundamentalists. While neoevangelicals were focused upon positive work, however, fundamentalists were focused upon neoevangelicals. They muttered their disapproval of the evangelical mainstream for not distancing themselves sufficiently from the most prominent neoevangelicals.
The more that moderate evangelicals [sic] shied away from the muttering, the more strongly fundamentalists expressed their disapproval. Many fundamentalists refused to acknowledge any middle ground or mediating position between themselves and the new evangelicalism. Moderate evangelicals were forced to choose….
By the end of the 1970s, the evangelical majority had staked out a position midway between separatist fundamentalism and neoevangelicalism. Leaders and institutions have wandered into and out of that position, but the position endures to this day. It is the position that we now call conservative evangelicalism. It has, however, been supplemented from a new and unexpected direction.
Before the 1980s, Southern Baptists were not reckoned as a part of the evangelical movement in America. Because they saw themselves as Baptists, they disliked the inter-denominationalism that characterized evangelicalism. Because they saw themselves as Southern Baptists, they disdained an evangelical movement that they viewed as a predominantly northern phenomenon.
That situation has changed. The conservative resurgence in the Southern Baptist Convention has brought many Southern Baptists into close contact with northern evangelicals. Conservative leaders like Albert Mohler and Mark Dever have found camaraderie and moral support in the evangelical movement. They have identified with it and they have found themselves welcome. Given the battles that they have fought against liberals and moderates, they have naturally aligned themselves with the conservative evangelicals. The degree of congruence is so high that these Southern Baptist leaders have become a defining force within the renascent conservative evangelical movement.
Many””perhaps most””Southern Baptists still do not consider themselves to be conservative evangelicals. They simply consider themselves to be Southern Baptists. Increasingly, however, many SBC leaders are forging an alliance with other evangelicals, and the alliance is a conservative one.
Consequently, today’s conservative evangelical movement combines ecclesiastical DNA from two kinds of leaders. It gets part of its heritage from the old proto-fundamentalism, traced through the moderate evangelicalism of the 1960s and 1970s. It gets another part of its heritage through the conservative resurgence in the Southern Baptist Convention.
Unlike neoevangelicals, conservative evangelicals (whether northern or southern) oppose theological apostasy and refuse to fellowship with apostates. Unlike fundamentalists, conservative evangelicals have been reluctant to issue public rebukes or declare public withdrawals from those who share the neoevangelical attitude toward apostates. This is the nub of the most important difference between these groups….
I, for one, don’t hesitate to embrace the “conservative evangelical” label. And I would view many conservative evangelicals as much closer in practice to fundamentalists, than most fundamentalists would acknowledge.
A while back I was reading through 
There may be a lot of good that conservative politics can offer America. Unfortunately for the Church, it can muddy the waters and make the Gospel message less clear.