But even if fewer Americans knew his name, it’s indisputable that at the time of his death, Mr. al-Baghdadi was a more significant figure in global terrorism than Mr. bin Laden was when he died. By the time Mr. bin Laden was killed, a decade after 9/11, he had become far removed from the day-to-day reality of his followers. Mr. bin Laden was in hiding in his compound in Abbottabad, Pakistan, cut off from the rapid changes that were taking place in the Arab world at the time, changes that would leave Al Qaeda reeling. Mr. al-Baghdadi, on the other hand, as we know from countless testimonies from captured ISIS members, still closely commanded an organization determined to revive his brutal caliphate.

Over his nine years as leader , Mr. al-Baghdadi built his group up from the ashes, after it was defeated by local Iraqi tribes with the backing of United States troops following the 2007 surge. He then moved quickly to take advantage of the Arab uprisings of 2011 to expand into neighboring Syria, at a time when Al Qaeda’s central leadership seemed disoriented by the pro-democracy wave sweeping the region. Three years later , he ascended the iconic Al Nuri Grand Mosque in Mosul to declare himself a caliph, ruling over one-third of Iraq and nearly half of Syria.

Mr. al-Baghdadi was central to the revival of global jihadism after the death of Mr. bin Laden. If it hadn’t been for him, Al Qaeda would have possibly continued along “a path to defeat,” as President Barack Obama described it after Mr. bin Laden’s death. The re-emergence of Al Qaeda after 2011 owed a great deal to Mr. al-Baghdadi’s expansion into Syria where he built up what was once touted as the group’s most successful branch: Jabhat al-Nusra, a group established after the Syrian uprising in 2011 that deserted ISIS in 2013 over disagreements with Mr. al-Baghdadi and pledged allegiance to Al Qaeda instead.

Following the death of Mr. bin Laden, Al Qaeda and other groups influenced by it have focused almost entirely on local wars, rather than on global jihad. International terrorism, especially in the West, has since become associated with ISIS. Which is why the fate of Mr. al-Baghdadi’s group, and international terrorism generally, depends largely on whether the United States seizes the historic moment of his death to keep the group down.

That the Islamic State can easily survive the loss of its top leader is not as straightforward a proposition as seems to be widely believed. Mr. al-Baghdadi’s death, almost exactly seven months after the obliteration of the physical caliphate he built, comes at an exceptionally bad time. The organization is still struggling to recover from the collapse of its caliphate and the deaths of many top leaders. It is fragile, caught somewhere between being a proto-state and a full-fledged insurgency.