If people scurry to do something, they do it as soon as they can. Pictures of starving children have sent many people scurrying to donate money. = rush. to move quickly with short steps, especially because you are in a hurry (hurry-scurry (18-20 centuries), from hurry)
When people or small animals scurry somewhere, they move there quickly and hurriedly, especially because they are frightened. The attack began, sending residents scurrying for cover