Instances of wanton violence by deranged attackers — whether in Nice or in Orlando, Fla. — are swiftly judged to be the work of terrorists. These judgments occur even when there is little immediate evidence that the attackers had direct ties to terrorist groups and when they do not fit a classic definition of terrorists as those who use violence to advance a political agenda.

“A lot of this stuff is at the fringes of what we would historically think of as terrorism,” said Daniel Benjamin, a former State Department coordinator for counterterrorism and a professor at Dartmouth College. But, he said, “the Islamic State and jihadism has become a kind of refuge for some unstable people who are at the end of their rope and decide they can redeem their screwed-up lives” by dying in the name of a cause.

Mr. Benjamin said this also led the news media and government officials to treat violence like the Nice attack differently from other mass attacks, like shootings at schools and churches that have been carried out by non-Muslims.

“If there is a mass killing and there is a Muslim involved, all of a sudden it is by definition terrorism,” he said.

The spectrum of terrorism is widening and now includes attacks loosely inspired by the Islamic State, those carried out by its affiliate groups and attacks directed by the group’s leadership. All have drawn public condemnation and concern, but the plots organized and executed by the Islamic State usually prompt greater concern from the authorities.