WASHINGTON — After a mob of Trump supporters stormed the Capitol last year, many Democrats and Republicans alike denounced the riot using terms like “terrorism.” But many Republicans later backed away from such condemnations as they sought to realign themselves with former President Donald J. Trump.

The highest-profile example yet came on Thursday, when the Fox News host Tucker Carlson accused Senator Ted Cruz of purposefully lying because he had continued to call the events of Jan. 6 a terrorist attack, including at a Senate hearing this week.

Mr. Cruz, Republican of Texas, apologized, calling his phrasing “frankly dumb” and saying that he was referring only to those rioters who assaulted the police. Mr. Carlson, who has insinuated that Jan. 6 may have been a plot to justify a “purge” of Trump-supporting “patriots,” rejected Mr. Cruz’s explanation, citing his consistent use of that term over the past year to describe the Capitol attack.

Here is a closer look at the charged debate over the use of the word.

What is terrorism?

Essentially, it is politically motivated violence.

Denouncing Mr. Cruz, Mr. Carlson declared that “by no definition” was Jan. 6 “a terror attack.” But Congress has enacted a statute that defines domestic terrorism as criminal offenses that are dangerous to human life, lack a foreign nexus and appear to be seeking “to influence the policy of a government by intimidation or coercion.”

According to that definition, some of the events of Jan. 6 “were acts of domestic terrorism, and that’s accurate regardless of whether it applies to each individual,” said Mary McCord, who served as a senior Justice Department national security official in the Obama administration and into the early Trump era.

She added, “We are talking about acts that were dangerous to human life and that were in violation of criminal laws, and they were certainly done to influence government policy because they were trying to prevent the counting of Electoral College votes.”

Did all the Jan. 6 rioters commit life-endangering crimes?

No. More than 700 people have been charged to date in connection with the Capitol attack, and they are accused of a spectrum of crimes. Just as only some have been charged with conspiracy and obstruction of an official proceeding, only some have been charged with violent offenses like assaulting police officers and destroying government property. Others have been charged only with nonviolent crimes, such as illegally entering a restricted building.

Mr. Cruz told Mr. Carlson that at the Senate hearing this week, he was not saying that “the thousands of peaceful protesters supporting Donald Trump are somehow terrorists.” Rather, he contended, he was merely using that term for people who attacked police officers — an explanation that Mr. Carlson, who agreed that such people should go to prison but maintained that they were not terrorists either, rejected.

On many occasions, Mr. Cruz has broadly called the assault on the Capitol an “act of terrorism” without specifically limiting his words to police assailants. In an interview a day after the riot, for example, he described the “terrorist attack” as “a traumatic experience for everyone in the building and everyone across the country,” and he referred to a rioter who “broke into the Senate chamber” and “did damage” as a “terrorist.”

Has anyone been charged ‘with terrorism’ over Jan. 6?

No. Mr. Carlson asked Mr. Cruz, “How many people have been charged with terrorism on Jan. 6?” The answer is zero — but that fact is deeply misleading.

Congress — despite establishing a legal definition for “domestic terrorism” — has not created any stand-alone federal crime called that. As a result, it is not possible for prosecutors to charge any of the Jan. 6 rioters “with terrorism” regardless of whether they committed terrorist acts.

Might some defendants nevertheless face longer sentences for terrorism-related offenses?

Yes. Dozens of defendants are facing charges that will give prosecutors the opportunity to ask for longer sentences by invoking the context of domestic terrorism. It is not yet clear how harsh prosecutors and judges will be when it comes time to sentence uncooperative defendants who insist on going to trial and then get convicted, rather than striking plea deals.

In one statute, for example, Congress deemed about four dozen offenses as eligible to count as a “federal crime of terrorism” if the acts were “calculated to influence or affect the conduct of government by intimidation or coercion, or to retaliate against government conduct.” Under sentencing guidelines, such a conviction can result in a much longer prison term.

The list includes destruction of government property, a charge that 44 defendants are facing so far, according to the Justice Department’s tally of the Jan. 6 cases. The list also includes a “weapon of mass destruction” charge that may be brought if the F.B.I. finds whoever put pipe bombs outside the Capitol Hill headquarters of both major political parties the night before the riot.

In addition, two defendants so far have been charged with making false statements. Under a separate law, prosecutors can ask for a sentence of up to eight years, rather than the normal five, if such lies involve domestic terrorism.

Why is the terrorism label subject to dispute?

Because nobody likes terrorists. And as a matter of ordinary speech, as opposed to legal definitions, drawing the line between “terrorism” and less pejorative terms for politically motivated violence can be notoriously subjective.

“Why did you use that word?” Mr. Carlson asked Mr. Cruz.

He accused the senator of playing into a characterization by “the other side” seeking to smear the “entire population” of Trump supporters as “foreign combatants,” likening it to labels like “insurrection” and “coup.”

Notably, during the nationwide protests after the police killing of George Floyd in Minneapolis in 2020, Mr. Carlson called on the Justice Department to charge “every single person caught on camera torching a building, destroying a monument, defacing a church” with terrorism.

“Call them what they actually are — domestic terrorists,” he said, adding: “That would be their new government-approved title. Once they’re charged, it’s official. In fact, they are literally, as a factual matter, accused terrorists. And that would change minds right away.”