Bush certainly described his War on Terror in ways that evoked a civilizational clash, pitting freedom-lovers against the totalitarian successors of the Nazis and communists. But he emphasized that Islam was not one of the clashing sides—that the terrorists had perverted the “peaceful teachings of Islam.” “Some call this evil Islamic radicalism,” he said in 2005. “Others militant jihadism. Still others Islamo-fascism. Whatever it’s called, this ideology is very different from the religion of Islam.”

Barack Obama has downgraded Bush’s War to a fight, and the enemy from Terror to specific terrorist groups. He rejects the notion of a clash of civilizations, both because he thinks it overestimates the threat of terrorism to the United States and because he doesn’t want to affirm the jihadists’ narrative of a struggle between Islam and infidels in the West. When a U.S. president uses “loose language that appears to pose a civilizational conflict between the West and Islam, or the modern world and Islam, then we make it harder, not easier, for our friends and allies and ordinary people to resist and push back against the worst impulses inside the Muslim world,” Obama told The Atlantic’s Jeffrey Goldberg.

Obama’s approach has produced a backlash that may shape policy in a Trump administration. For years now, Republicans have condemned Obama’s avoidance of the term “radical Islam,” arguing that it represents the president’s failure to properly assess and address the threat. Radical Islam, Obama’s critics contend, is what it sounds like: radicalism rooted in the religion of Islam. Where Obama sees “violent extremism,” his critics see militant religiosity. Where Obama sees a clash within Islamic civilization—between a tiny faction of fanatics and the vast majority of Muslims—his critics see a clash between Western civilization and a small yet significant segment of the Muslim world. Where Obama sees a weak enemy that is getting weaker, his critics see a strong enemy that is getting stronger. Where Obama sees limits to what the U.S. can do on its own to eradicate radical interpretations of Islam, his critics see an appalling lack of effort by the U.S. government. Where Obama sees a serious but manageable national-security threat, his critics see an ideological and civilizational challenge to the free world.

Trump has gone further than many other Republican leaders in advancing the counterargument to Obama—not just in his proposed policies, like banning or severely restricting Muslim immigration to the United States, but also in his rhetoric. “I think Islam hates us,” Trump said earlier this year. Asked if he was referring to “radical Islam,” he responded, “It’s radical, but it’s very hard to define. It’s very hard to separate. Because you don’t know who’s who.”

Several members of Trump’s emerging team have described the threat in similarly stark and broad ways. “We’re in a world war against a messianic mass movement of evil people, most of them inspired by a totalitarian ideology: Radical Islam. But we are not permitted to speak or write those two words, which is potentially fatal to our culture,” writes Michael Flynn, Trump’s pick for national-security adviser, in a book he published this summer with the conservative writer Michael Ledeen.