The string of bombings in Austin this month revived an ongoing debate over how the government investigates and prosecutes terrorism, revealing a split between the way many Americans think about terror and the way U.S. law defines it.

After package bombs killed two people and injured several others, police cornered the suspect Wednesday morning on the side of a highway, where authorities say he detonated a homemade bomb as officers closed in. Authorities on Friday ruled his death a suicide caused by “multiple penetrating shrapnel injuries,” according to Dain Johnson, a justice of the peace in Williamson County, Tex., where the bomber died.

After his death there was widespread relief, but law enforcement officials also found themselves dealing with a familiar question: Why don’t they call this terrorism?

Law enforcement officials have repeatedly said the Austin bomber terrorized the community. But at the same time, they made clear they have not found indicators that he was inspired by any foreign terrorist groups. Nor, they said, did his self-made confession video indicate he was motivated by hate for a particular race or group.

“Some people will say it’s terrorism, because it caused terror in that community. I don’t look at it as terrorism, because there’s no organization behind it,’’ said Malcolm Brady, a former assistant director for the federal Bureau of Alcohol, Tobacco, Firearms and Explosives. “This is a single individual that was more than likely mentally unstable about something, so he blew things up. . . . He’s not a terrorist.”

Two strands of federal criminal law define violent crimes intended to terrorize or intimidate large groups of people.

Federal anti-terrorism laws focus on attacks inspired by foreign terrorist groups, arising out of an era when such groups hijacked or destroyed planes. Domestic civil rights and hate crimes statutes seek to punish those who try to harm people because of their race or group, arising in part out of cases of the 1950s and 1960s.

But in an era when a disturbed person with a weapon can kill randomly in public, the legal distinctions between terrorism, hate crime and a killing rampage can seem less meaningful.

“A lot of people feel like there’s a double standard being used,” said Adam Lankford, a professor at the University of Alabama and an expert on mass killers. “And it makes them skeptical of what law enforcement says, because they’re seeing it as, well, if this guy’s Muslim you’re going to call him a terrorist, and if he’s not, you’re going to use some other label. When in fact, it’s really putting law enforcement in a tricky position, because they’re really just responding to a definition they’ve been given and trying to apply it accurately.”

Lankford said that whatever mass killers’ particular motivations might be, they tend to share certain psychological traits that may be more important than their agendas. Such traits include a sense of victimization, a pattern of seeking negative attention, and being suicidal or not caring whether they live.

In the Austin case, police have not officially declared a motive, saying only that the bomber expressed anger with his life during a confession recorded on his phone. Brian Manley, the interim Austin police chief, said Wednesday that Mark Anthony Conditt left behind a 25-minute recording “talking about challenges in his personal life that led him to this point.”

This description prompted some to criticize Manley and argue that he was being overly sympathetic toward the bomber. The chief said later that his remarks were only “a reflection of what [the bomber’s] comments were. They are not my belief; they are not my opinion.”

“In no way am I going to be sympathetic towards someone who murdered people in our community,” Manley told KVUE, a Texas television news station, on Thursday. “My opinion is that he created terror in our community by his actions and he stole lives from our community.”

Police have declined to release the 25-minute recording publicly, citing the ongoing investigation into the bombings, but Lankford said that what authorities have described publicly matches what often emerges about mass killers in other contexts.

While the Washington-area sniper killings terrified the D.C. region in 2002, some authorities said that the attacks appeared to be terrorism. President George W. Bush said that the shootings were “a form of terrorism, but in terms of the terrorism we think of, we have no evidence.”

Ronald Knight, the then-sheriff of Spotsylvania County, Va., where two of the sniper attacks occurred, said at the time: “To me, it is terrorism. I’m not going to stand here and say it’s Al Qaeda. Whether it’s a local terrorist or a global terrorist, it is striking terror in people’s hearts.”

After those attackers were identified, officials said they found nothing tying them to organized terrorism. Yet terrorism played a role in what followed: Virginia used its anti-terrorism law, passed after the 9/11 attacks, for the first time, in the trial of D.C. sniper John Allen Muhammad; he was executed in 2009.

Many other states have their own terrorism statutes. After police said a white Maryland man admitted to fatally stabbing a black man in New York City and intending to kill many more, prosecutors indicted him on two counts of murder as an act of terrorism.

Shooting rampages also often conclude with the attackers facing police gunfire or killing themselves. An FBI study of shootings between 2000 and 2013 found that in nearly half of the incidents studied, the attackers committed suicide; in many other cases, attackers were killed or wounded by law enforcement officials.

“Violence now is not just a symbolic statement for the traditional terrorist,” said Brian Levin, who runs the Center for the Study of Hate and Extremism at California State University at San Bernardino. It is unfortunate, he said, but “violence has currency in our society, and it’s not just for the traditional terrorist. It’s for anyone who thinks they have some kind of personal grievance.”

Levin also said that even without directly knowing the Austin bomber’s motivation, the explosions were different from a more traditional crime such as robbing someone.

“These attacks were symbolic in their own way,” he said. “There was a goal to kill, but also to disrupt the community.”

While people may have felt terrorized in Austin and Parkland, the crimes that caused their fear still might not meet the legal criteria for terrorism, he said.

“Just because something has a terroristic effect might not make it necessarily have the critical mass of ideology that is attached to the traditional terrorist definition,” Levin said. “If all violence is labeled as terrorism, then the definition fails as well.”