Mr. Breivik, in planning his 2011 attack, appeared to draw ideologically on European far-right websites on which he was an active commenter, according to a research paper by Raffaello Pantucci, a terrorism expert at King’s College London. Mr. Breivik wrote a 1,500-page manifesto that, like the propaganda of the Islamic State, provides ideological justification and some tactical advice for anyone interested in following his model.

At a time when terrorism is a major issue in Western politics, defining something as terrorism is not just a matter of determining motive. It is a political statement in itself.

Consider 22-year-old Dylann Roof, who last year killed nine people at a predominantly black church in South Carolina. A Facebook photo of Mr. Roof showed him wearing flag patches — one from apartheid-era South Africa, the other from white-ruled Rhodesia — that have been adopted by white supremacists. He later said he had hoped to ignite a race war.

When the Justice Department announced charges against Mr. Roof, none mentioned terrorism. Legal scholars say that this accurately reflects federal law, which classifies only certain acts, such as airplane hijackings, as terrorism. But the decision appalled many African-Americans, who saw it as part of a pattern of playing down white supremacist violence against them.

This spoke to the significance of labeling something as terrorism, which implies that the attack represents a larger threat — and thus compels action against that threat.

This is why many Republicans have criticized President Obama for, they say, being too slow to label an attack as terrorism, which they see as an excuse to avoid action.

But it is also why Muslim and civil rights groups worry that lone madmen are more likely to be termed terrorists if they are Muslim, which they say encourages fear and suspicion of Muslims. Anti-Muslim attacks are rising in the United States and Europe, highlighting the consequences of that fear.