Making sense of the carnage unleashed in the name of Islamic State in the West, from Paris and Brussels to Orlando, boils down to a chicken-and-egg problem that bedevils governments and terrorism scholars.

The killers in all these atrocities were, by definition, radicals, and all of them had pledged allegiance to Islamic State. But is the main threat facing the West the radicalization of Islam—or the Islamization of radicalism?

Different...