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WASHINGTON — One of the currents running through the presidential campaign has been a tacit but fundamental question: After 11 years of the war on terror, what kind of threat does Al Qaeda pose to America? 

The candidates offered profoundly different answers during their final debate last week, with President Obama repeating his triumphant narrative of drone attacks and dead terrorists, and Mitt Romney warning darkly about Islamists on the march in an increasingly hostile Middle East.

In a sense, both are true. The organization that planned the Sept. 11 attacks, based in Afghanistan and Pakistan, is in shambles; dozens of its top leaders have been killed since Mr. Obama assumed office, and those who remain appear mostly inactive.

At the same time, jihadists of various kinds, some identifying themselves with Al Qaeda, are flourishing in Africa and the Middle East, where the chaos that followed the Arab uprisings has often given them greater freedom to organize and operate. The death of J. Christopher Stevens, the American ambassador to Libya, in September during an assault by armed Libyan jihadists on the American mission in Benghazi has driven that home to the American public.

But there is an important distinction: most of the newer jihadist groups have local agendas, and very few aspire to strike directly at the United States as Osama bin Laden’s core network did. They may interfere with American interests around the world — as in Syria, where the presence of militant Islamists among the rebels fighting the government of Bashar al-Assad has inhibited American efforts to support the uprising. But that is a far cry from terrorist plots aimed at the United States itself.

“In a lot of ways we’ve gone back to the way the world was before Sept. 11,” said Brian Fishman, a research fellow in counterterrorism at the New America Foundation. “It’s local jihadi groups focused on projects within their own countries, even if they sometimes maintain the rhetorical framework of Al Qaeda and its global struggle.”

While these local groups may have benefited in the short term from the turbulence that followed the Arab Spring uprisings, they have also suffered an ideological blow that could make it far more difficult to recruit young followers. Peaceful protest movements brought down dictatorships in Tunisia and Egypt, and there, as in the more violent conflicts in Libya and Yemen, the United States was on the side of change.

The idea of attacking the United States, “the far enemy” in jihadist parlance, was always unpopular for many Islamic radicals, whose chief goal was replacing their own governments with theocracies. The concept became more unpopular after the Sept. 11 attacks when Osama bin Laden and his followers were driven out of their sanctuary in Afghanistan. In the following years, Al Qaeda’s affiliates in Iraq and Saudi Arabia did the brand considerable harm by killing large numbers of Muslims, although killing American soldiers in Iraq, where those troops were seen as Crusader-like occupiers, still met with wide approval.

What Al Qaeda retains is a mystique, the legend of a small band of warriors who took on an empire and struck a devastating blow. That mystique still has tremendous appeal, even for insurgents who differ with Al Qaeda’s methods or its focus on attacking America.

Recent years have seen the proliferation of jihadist movements that may take some inspiration from Al Qaeda, but have greatly divergent goals. In Nigeria, the radical Islamist group Boko Haram has killed thousands of people in the past few years in its struggle to overthrow the government and establish an Islamic state. There, the struggle is largely sectarian; Boko Haram has struck mostly at Christians and burned churches.

Jihadists now control Mali’s vast north, as Mr. Romney mentioned more than once in the last debate, and have links to an older group officially affiliated with Al Qaeda that grew out of Algeria’s civil conflict in the 1990s. Although these groups are well armed and dangerous, some appear to be more criminal than ideological, focused on kidnapping and drug smuggling. Jihadists have also gained strength in Egypt’s Sinai Peninsula, just across the border from Israel.