Hours after a truck ploughed along a Manhattan bike path on Tuesday, Americans returned to a debate that has become a vessel for some of the most contentious questions dividing an increasingly polarised society: When is an attack terrorism?

A month ago, when a gunman opened fire on a crowd of concertgoers in Las Vegas, killing dozens and wounding hundreds, the attack was not broadly branded an act of terrorism. But that label was immediately attached to the attack on Tuesday that killed eight people, setting off another round of a fierce national debate.

On the surface, this could be considered a straightforward question of motive. Terrorism is defined as an attack on civilians meant to frighten a larger community for political purposes.

But the new generation of Islamist terrorism, conducted by individuals citing far-off inspiration, has blurred the distinctions between terrorist and disturbed loner. So have recent mass shooters who show signs of both mental illness and an attachment to vague ideological causes.

As a result, terrorism is often in the eye of the beholder, determined as much by the attacker as by the community that is targeted, which must decide whether the attack represents a broader threat requiring a response.

Each attack, then, quickly sets off a zero-sum debate over the related issues of gun control, immigration or religious tolerance — some of the most divisive issues in the country — litigated in a moment of national duress.

The Las Vegas attack, for some Americans, typically those on the left, represented the terrorism of unchecked gun laws.

Classifying the Las Vegas attack as terrorism might mean classifying guns as national threats requiring a response. The right would see this as an attempt to tar all gun owners and conservatives.

Attacks like the one in New York, led by a man from Uzbekistan who shouted “Allahu akbar,” are seen by many on the right as stemming from the wider threat of uncontrolled Muslim immigration. If it is an act of terrorism, as Mayor Bill de Blasio and others have defined it, then the attacker cannot be dismissed as a disturbed loner.

More than 16 years after the 11 September attacks, many Americans, particularly on the left, are questioning the readiness with which lone Muslims are defined as terrorists while lone non-Muslims are deemed “mass shooters.”

Even if the label fits in individual cases, they say, the inconsistency suggests a tendency to see Muslims as part of a hostile fifth column and white male killers as exceptions.

Because mass killings are such acute moments of public horror, this is not an area in which people can easily agree to disagree. The differing responses can seem to impose a hierarchy of victims, in which those killed by one sort of attacker are deemed to matter more than others, and a hierarchy of perpetrators, sorted by those seen as posing the greater threat.

What can seem like a simple matter of definition quickly divides between different factions arguing for the primacy of their own world view, at a moment when it seems simultaneously most urgent and least appropriate.

Each attack deepens these divides. The events cause visceral terror for many, and can feel like evidence that their worst fears are coming true — and that the other half of society is conspiring to make them unsafe by refusing to recognise the threat.

After the attack in New York on Tuesday, President Donald Trump posted a string of tweets that connected the driver to immigration policy. He said he had ordered the Department of Homeland Security to “step up our already Extreme Vetting programme,” and called for an end to a diversity visa lottery programme for immigrants.

“Being politically correct is fine, but not for this!” he wrote.

Those on the left, particularly those concerned about rising attacks on Muslims, worry about an attempt to further marginalise Muslim Americans at a moment when they are especially vulnerable.

“Man screams ‘Allahu Akbar’ & kills people. Media: Terrorism!” Nathan Lean, the author of a book on Islamophobia, wrote on Twitter. “White guy slays 56 in Las Vegas with battle-ready weapons. Media: Crickets.”

These debates have grown especially contentious since 2015, when Dylann Roof, a South Carolina man who had publicly espoused white supremacy, killed nine people at a mostly black church in Charleston.

The Black Lives Matter movement had spent two years campaigning against violence against African-Americans, particularly those killed in encounters with police. Roof’s attack, they argued, demonstrated the threat facing black people.

If Islamist terrorism had inspired national mobilisations and sweeping policy changes, they argued, so should violence against blacks. And the crime appeared to neatly fit terrorism’s legal definition.

The argument expressed growing worries on the left that the word “terrorism” had become racially and religiously charged, used predominantly to describe attacks by Muslims on non-Muslims.

This fed into larger debate over whether some victims of terrorism were granted more protection than others based on who targeted them or why — and whether politicians were understating certain forms of terrorism.

When a Department of Homeland Security report on right-wing extremism leaked in 2009, it prompted accusations that Democrats were persecuting conservatives. The report was withdrawn and the office that had produced it quietly dismantled.

Las Vegas shooting – in pictures Show all 15 1 /15 Las Vegas shooting – in pictures Las Vegas shooting – in pictures People scramble for shelter at the Route 91 Harvest country music festival after gun fire was heard Getty Las Vegas shooting – in pictures People carry a person at the Route 91 Harvest country music festival after shots were fired David Becker/Getty Las Vegas shooting – in pictures People run from the Route 91 Harvest country music festival after gun fire was heard David Becker/Getty Las Vegas shooting – in pictures A handout photo released via Twitter by Eiki Hrafnsson (@EirikurH) showing concertgoers running away from the scene (C) after shots range out at the Route 91 Harvest festival on Las Vegas Boulevard EPA/Eiki Hrafnsson Las Vegas shooting – in pictures People lie on the ground at the Route 91 Harvest country music festival after hearing gun fire Getty Las Vegas shooting – in pictures A man in a wheelchair is taken away from the Route 91 Harvest country music festival after hearing gun fire David Becker/Getty Las Vegas shooting – in pictures People stand on the street outside the Mandalay Bay hotel near the scene of the Route 91 Harvest festival on Las Vegas Boulevard EPA/Paul Buck Las Vegas shooting – in pictures FBI agents confer in front of the Tropicana hotel-casino after a mass shooting during a music festival on the Las Vegas Strip Reuters/Las Vegas Sun/Steve Marcus Las Vegas shooting – in pictures Las Vegas police run by a banner on the fence at the Route 91 Harvest country music festival grounds after shots were fired David Becker/Getty Las Vegas shooting – in pictures An injured person is tended to in the intersection of Tropicana Ave. and Las Vegas Boulevard after a mass shooting at a country music festival Ethan Miller/Getty Las Vegas shooting – in pictures Metro Police officers pass by the front of the Tropicana hotel-casino after a mass shooting at a music festival on the Las Vegas Strip Reuters/Las Vegas Sun/Steve Marcus Las Vegas shooting – in pictures A woman sits on a curb at the scene of a shooting outside of a music festival along the Las Vegas Strip AP/John Locher Las Vegas shooting – in pictures A cowboy hat lays in the street after shots were fired near a country music festival in Las Vegas Getty Las Vegas shooting – in pictures Las Vegas Metro Police and medical workers stage in the intersection of Tropicana Avenue and Las Vegas Boulevard South after a mass shooting at a music festival on the Las Vegas Strip Reuters/Las Vegas Sun/Steve Marcus Las Vegas shooting – in pictures Sheriff Joe Lombardo (2-R) speaking during a press briefing in the aftermath of the active shooter incident on Las Vegas Boulevard EPA

The same year as Roof’s attack, Trump’s presidential campaign gained ground on a different argument that identity politics had led certain forms of terrorism to be played down. In a campaign statement, Trump called for “a total and complete shutdown of Muslims entering the United States” to protect from “people that believe only in Jihad, and have no sense of reason or respect for human life.”

Defining terrorism, then, has become another way of debating who belongs and whose concerns matter — and at a moment of perceived danger, when listening is hardest and shouting can feel necessary. It has become a perfect vessel for Americans’ growing tendency to see their political opponents as not merely fellow citizens with whom they disagree, but as threats to their safety and security.

That is a recipe for increased polarisation and hostility at a moment when Americans are already dangerously divided.