WASHINGTON — In the absence of any hint of a motive in the Las Vegas massacre, President Trump late Monday morning called it “pure evil.” Notably, he avoided the word “terrorism.”

The gunman, Stephen Paddock, a 64-year-old with no significant criminal history and no obvious ideological motive, remained a blank space, offering little for Americans who crave an explanation for the tragedy to seize upon.

But that did not deter a daylong jumble of industrious, contradictory and often self-interested speculation.

Early in the day, right-wing websites named the wrong man as the gunman, labeling him “another angry far-left shooter,” in the words of the Gateway Pundit. A conservative Las Vegas radio personality, Wayne Allyn Root, told his 110,000 Twitter followers: “This is real thing. Clearly coordinated Muslim terror attack” — an early guess given a brief boost by a claim of responsibility from the Islamic State.

Then the F.B.I. knocked down the Islamic State angle, noting that the group has a history of false claims. The guessing game resumed: Was it a plot by “deep-state Democrats” (Alex Jones of the conspiracy site Infowars) or perhaps divine punishment for the “profound disrespect” shown to Mr. Trump and the national anthem (the religious broadcaster Pat Robertson)? Was it something to do with country music, given the concert crowd Mr. Paddock targeted? Could it be linked in any way to the long-ago history of Mr. Paddock’s father as a bank robber on the F.B.I.’s most-wanted list?

“Stephen Paddock motive” ranked high among Google searches, and it remained uncertain whether more evidence would fill the void about what drove his killing rampage or the slaughter would drift into history as one more act of American mass violence to elude easy categorizing.

Mass killing of innocents, even on the scale of Las Vegas, does not automatically meet the generally accepted definition of terrorism, which requires a political, ideological or religious motive. But beyond that academic analysis, in political debate in a polarized country, the word “terrorism” is also a verbal weapon, freely wielded — especially when the accused is Muslim.

“The label is so powerfully pejorative and carries so much weight,” said Martha Crenshaw, a terrorism expert at Stanford’s Center for International Security and Cooperation.

The first reports of any mass attack summon not only a general sense of grief, but anxieties and wishes in specific American subgroups: Muslim Americans pray that the attacker does not share their faith, for instance; conservatives and liberals alike want the assailant to turn out to be a member of their political opposition.

“In today’s political climate, it’s so polarized that people are hoping it’s not pinned on their side,” Ms. Crenshaw said. As a political progressive, she admitted to a passing feeling of dread on Monday that the gunman might come from the left.

More cynical observers of American politics may feel that Mr. Paddock’s advanced age, white race and non-Muslim religious background make it less likely that he will be tagged a terrorist, whatever may emerge about his politics.

And this gruesome tragedy, perhaps the deadliest single shooting episode in American history, quickly and predictably reopened a debate on gun control. If Mr. Paddock’s purpose was uncertain, his choice of weapons was unmistakable.

The tussle over what terrorism is dates back to the beginning of its modern history, said David C. Rapoport, the dean of American historians of terror. He said a Russian radical who shot the governor of St. Petersburg in 1878, Vera Zasulich, was asked at trial why she laid down her gun after merely wounding her target.

“I’m not a criminal — I’m a terrorist,” she declared, he said, suggesting that she had made her political point and felt no need to pile on with lethal violence.

“That’s not our conception of terrorism,” said Mr. Rapoport, a retired professor at the University of California, Los Angeles, and founding editor of the journal Terrorism and Political Violence.

Mr. Rapoport’s well-known taxonomy identifies four major waves of terrorism since the 1880s: the anarchists; anticolonial activists; leftists around the time of the Vietnam War; and since 1979, religious zealots, including non-Muslims. He said each of the earlier waves lasted about 40 years, and that he expected the period of religious terrorism to fade by 2025.

But in every case, the perpetrators had a clear ideological agenda. They were also overwhelmingly young, Mr. Rapoport said. Mr. Paddock so far seems to fit none of the patterns. His age, a year short of qualifying for Medicare, is especially perplexing.

Still, the phenomenon of mass shooting, whether or not it properly carries the terrorist label in a particular case, is a recognizable American phenomenon. And from the point of view of potential victims, the crucial factor may not be a specific ideological motivation but the decision to target random, innocent people.

Homicides in the United States rose more than 8 percent in 2016, to 17,250, the F.B.I. reported last month. But most killings by far have a clear answer to the question of why. Many are crimes of passion; many others accompany robberies, sexual assaults or disputes inside the drug trade or other criminal enterprises.

Shooting down systematically from a hotel window on a crowd of 22,000 people enjoying a concert is a different matter, said John Mueller, a political scientist at Ohio State who studies terrorism. Even if that name does not apply, Mr. Paddock’s baffling attack unquestionably spread terror far beyond Las Vegas.

“The question people ask about this kind of violence is, Can I imagine myself in the situation of the victims?” Mr. Mueller said. “In this case, the answer is absolutely yes.”