Without a firmly established motive, no one Thursday quite knew how to categorize the San Bernardino massacre. Terrorism? Workplace violence? A hybrid of the two?

If terrorism, why target co-workers at an obscure holiday party in a small city that many Americans can’t find on a map? And if the shooters were, in fact, radicalized Islamists, pursuing a jihadist agenda, were they essentially freelancing, or part of a more complex operation that might have also had other targets?

If this was workplace violence, why the enormous arsenal of bullets and the dozen pipe bombs in the rented home?

Every mass shooting has its peculiar elements, but this one stands out as particularly unusual. The two suspects, both slain by police in a wild gun battle four hours after the massacre, were husband and wife. They left their 6-month-old baby with a grandmother prior to the shooting spree.

Mass shootings almost invariably involve a single gunman, often someone in the throes of mental illness or in some way isolated from mainstream society. But as many people have noted, the shooters in this case seemed to be living the good life.

Police identified the two deceased suspects as Syed Rizwan Farook, a Chicago-born American, age 28, and Tashfeen Malik, 27, his Pakistani-born wife. Farook had traveled abroad last year, visiting Pakistan and Saudi Arabia, and he and his wife married back in the United States, police said. Law enforcement authorities have said the two were not on any watch lists; so far there is little direct evidence that they were radicalized.

“It’s very odd,” a senior U.S. law enforcement official said Thursday. “It appears they were a happy couple of the Muslim faith.”

“Based on what is known now about the case, it certainly is unusual and does not fit neatly into any of the traditional models of violence that we’re familiar with,” said Mark Pitcavage, director of the Center on Extremism for the Anti-Defamation League.

The motive for Wednesday’s massacre, and the associated terminology, has implications for law enforcement, the justice system, the political debates that will inevitably come out of this, and even for the psyches of Americans wondering what, exactly, they’re dealing with.

“It is possible that this is terrorist-related, but we don’t know,” President Obama said during somber remarks Thursday morning in the Oval Office. “It is also possible that this was workplace-related.”

A few minutes later, he added, “There may be mixed motives involved in this, which makes the investigation more complicated.”

What to call a crime like this, and how to categorize it, is not merely a semantic issue. The FBI, which has authority to investigate potential acts of terrorism, said Thursday that it had taken over the case from local and county law enforcement officials. But the FBI, like Obama, has not publicly said whether it considers this a terrorist attack.

“It would be irresponsible and premature for me to call this terrorism,” David Bowdich, assistant director of the FBI’s Los Angeles field office, said Thursday.

The government has numerous legal definitions of terrorism, but the National Institute of Justice admits up front, “The search for a universal, precise definition of terrorism has been challenging for researchers and practitioners alike.”

 The U.S. Code defines it as “premeditated, politically motivated violence perpetrated against noncombatant targets by subnational groups or clandestine agents, usually intended to influence an audience.” The FBI has a different definition: “The unlawful use of force or violence against persons or property to intimidate or coerce a government, the civilian population, or any segment thereof, in furtherance of political or social objectives.”

Pitcavage said his organization defines terrorism as “major criminal acts of violence against people or property committed by non-state actors in non-military situations in furtherance of political, social, religious, or other similar goals.”

There continue to be debates about what to call incidents such as the shooting last Friday at the Planned Parenthood clinic in Colorado Springs, with some advocates against gun violence arguing that it should be classified as domestic terrorism.

Terminology can also have long-standing political ramifications. Obama and his administration, including his former secretary of state, Hillary Clinton, have been slammed repeatedly for not immediately labeling the September 2012 attacks on U.S. personnel in Benghazi, Libya, as “terrorist” attacks. House Republicans have grilled Clinton on what she knew and when she knew it, with Republicans arguing that the Obama administration tried to downplay the terrorism angle for political reasons in the run-up to Obama’s 2012 reelection bid.

After the Paris attacks last month, a number of Republican presidential candidates excoriated prominent Democrats for being unwilling to use the phrase “radical Islamic terrorism.” But Hillary Clinton said it would be a mistake to use such terminology, saying the United States needs to improve relations with Muslim countries. She said the United States is “at war with violent extremism” and “people who use their religion for purposes of power and oppression.”