Here is a simple sketch by Joseph Ledoux of the difference between fear and anxiety:
You are taking a walk in the woods ― pleasant, invigorating, the sun shining through the leaves. Suddenly, a rattlesnake appears at your feet. You experience something at that moment. You freeze, your heart rate shoots up and you begin to sweat ― a quick, automatic sequence of physical reactions. That reaction is fear.
Human anxiety is greatly amplified by our ability to imagine the future, and our place in it.
A week later, you are taking the same walk again. Sunshine, pleasure, but no rattlesnake. Still, you are worried that you will encounter one. The experience of walking through the woods is fraught with worry. You are anxious.This simple distinction between anxiety and fear is an important one in the task of defining and treating of anxiety disorders, which affect many millions of people and account for more visits to mental health professionals each year than any of the other broad categories of psychiatric disorders.
Scientists generally define fear as a negative emotional state triggered by the presence of a stimulus (the snake) that has the potential to cause harm, and anxiety as a negative emotional state in which the threat is not present but anticipated. We sometimes confuse the two: When someone says he is afraid he will fail an exam or get caught stealing or cheating, he should, by the definitions above, be saying he is anxious instead.