The two groups share a nihilistic worldview, a loathing for modernity and for the West. They subscribe to the same perverted interpretations of Islam. Other common traits include a penchant for suicide attacks, and sophisticated exploitation of the Internet and social media. Like ISIS, several al-Qaeda franchises are interested in taking and holding territory; AQAP has been much less successful at it.

The main differences between al-Qaeda and ISIS are largely political—and personal. Over the past decade, al-Qaeda has twice embraced ISIS (and its previous manifestations) as brothers-in-arms. Each time, al-Qaeda leader Ayman al-Zawahiri has advised the Iraqi-Syrian group to restrain itself, only to be told to mind his own business. But as recently as last summer, Zawahiri was calling for reconciliation between the two groups. This time, he seems to have simply been ignored.

One bone of contention is the claim by ISIS’s leader, Abu Bakr al-Baghdadi, to the title of “caliph” of Islam. While Zawahiri was willing to acknowledge the so-called Islamic State as an “emirate”—an independent political entity—he has refused to recognize Baghdadi’s “caliphate.” In turn, Baghdadi doesn’t regard Zawahiri as the inheritor of Osama bin Laden’s mantle.

But further down the al-Qaeda chain of command, there’s a great deal of confusion over how ISIS should be regarded. Leaders of various al-Qaeda franchises have both congratulated ISIS for its successes in Syria and Iraq, and condemned its religious posturing.

In practical terms, the two groups are vying for common resources—and ISIS is clearly winning. Baghdadi’s recent successes on the battlefield make his group the more attractive of the two, and young jihadist wannabes who were previously drawn to the al-Qaeda training camps in Yemen and Somalia are now much more likely to join ISIS in Syria and Iraq. Donations to the jihadist cause are much more likely to make their way into Baghdadi’s war chest than Zawahiri's.

But that doesn’t automatically mean al-Qaeda and ISIS are enemies—their differences don’t seem deep enough for government and counterterrorism agencies to exploit. While their top leaders disagree on points of order, the groups are able to coexist and occasionally cooperate. In Syria, for instance, al-Qaeda (and its affiliate, the Khorasan Group) is able to fight alongside ISIS.

Sadly, that spirit of cooperation extended to Paris last week.

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