Fear is an emotion that elicits the "fight-or-flight" response of the autonomic nervous system. It is an immediate (uncontrollable) response to a direct danger - such as a rattlesnake, a gun pointed at your head, or a fast car driving right at you. Fear is generally a helpful response that allows you to protect or remove yourself from the imminent peril.
Sometimes the fear response can occur in the absence of any obvious stimulus - this can lead to a panic attack. Panic attacks are terrifying physiological and psychological events in which your autonomic nervous system ramps you up for fight-or-flight. Often, the person becomes terrified that they are dying - usually of a heart attack. Like intense fear, the heart starts pounding, adrenaline flows, breathing races. Sometimes the victim will run from the room - perhaps to a hospital or perhaps with no direction at all - to escape the unseen threat.