Fear is an important and valuable emotion. It warns us about danger and helps us to keep safe. However, fear is only useful if it protects us from real threats, and is in proportion to the danger. If fear starts to control you, or prevent you from taking any risks, then it becomes very harmful. Anxiety is a form of fear, but is a more enduring and pervasive state. With fear, the cause of the fear is clear, whereas with anxiety, the cause may not be as clear, or may not be known at all.
Anxiety disorders are psychological conditions in which anxiety becomes crippling. Panic attacks, phobias, Post-Traumatic Stress Disorder, and Obsessive Compulsive Disorder are examples of anxiety disorders. Read more here.
Everybody worries to some extent. Worrying is thinking anxiously about future events. Obviously, thinking fearfully about something in the future does not accomplish much. It is completely different to preparing oneself or problem solving, in which one thinks about a problem in a productive way. Worry may be an indication that you should do some problem solving. If there is really nothing you can do to solve the problem, then other techniques such as relaxation and thought-stopping may be helpful.
Generalised Anxiety Disorder (GAD) is a psychological disorder in which a person worries all the time to an excessive and debilitating extent. GAD may be treated with psychological therapy and/or medication.
Shyness is an anxious response to unfamiliar social situations. Most people feel shy in some situations sometimes. However some people feel their shyness to be a problem. Apart from the discomfort it causes, it may prevent them from making contact with people they would like to get to know, make it hard for them to assert themselves, and limit their social and other opportunities. Extreme shyness can become a disorder known as Social Phobia, which can prevent a person from even leaving their own home for fear of the social contact that it may entail.