Hours after a truck plowed 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 polarized 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.