Actually the term neocon was coined by their founder Irving Kristol to desribe 60's liberal intelligisia who were as he put it "mugged by reality."
Even I, frequently referred to as the "godfather" of all those neocons, have had my moments of wonderment. A few years ago I said (and, alas, wrote) that neoconservatism had had its own distinctive qualities in its early years, but by now had been absorbed into the mainstream of American conservatism. I was wrong, and the reason I was wrong is that, ever since its origin among disillusioned liberal intellectuals in the 1970s, what we call neoconservatism has been one of those intellectual undercurrents that surface only intermittently. It is not a "movement," as the conspiratorial critics would have it. Neoconservatism is what the late historian of Jacksonian America, Marvin Meyers, called a "persuasion," one that manifests itself over time, but erratically, and one whose meaning we clearly glimpse only in retrospect.
Neoconservatism is the first variant of American conservatism in the past century that is in the "American grain." It is hopeful, not lugubrious; forward-looking, not nostalgic; and its general tone is cheerful, not grim or dyspeptic. Its 20th-century heroes tend to be TR, FDR, and Ronald Reagan. Such Republican and conservative worthies as Calvin Coolidge, Herbert Hoover, Dwight Eisenhower, and Barry Goldwater are politely overlooked.
But they are impatient with the Hayekian notion that we are on "the road to serfdom." Neocons do not feel that kind of alarm or anxiety about the growth of the state in the past century, seeing it as natural, indeed inevitable.
People have always preferred strong government to weak government, although they certainly have no liking for anything that smacks of overly intrusive government. Neocons feel at home in today's America to a degree that more traditional conservatives do not. Though they find much to be critical about, they tend to seek intellectual guidance in the democratic wisdom of Tocqueville, rather than in the Tory nostalgia of, say, Russell Kirk.
Although neoconservatism and traditional conservatism overlap in many areas, the above quotes make it clear that there is a profound difference between the two.