Social Anxiety Disorder
Social Anxiety Disorder (also called Social Phobia) is a kind of panic disorder.  It's most easily described as extreme shyness, but it goes beyond that to include panic attacks when placed in certain social settings.  Some cases are extreme and even the thought of being in a social setting causes panic.   Information from the NAMI (National Alliance for the Mentally Ill) fact sheet on Social Anxiety Disorder is below.
Panic disorder
Those suffering from panic disorder experience reoccurring and unexpected panic attacks-instances of extreme fear or discomfort that start abruptly and build to a rapid peak, usually within ten minutes. Panic attacks are characterized by such physical symptoms as heart palpitations, sweating, trembling, shortness of breath, the sensation of choking, chest pain, nausea, dizziness, disorientation, fear of losing control or dying, numbness, chills, and hot flushes. Additionally, panic attacks are usually accompanied by a sense of looming danger and the strong desire to escape. Attacks can be brought on by specific triggers or can occur "out of the blue." The frequency of attacks tends to vary according to the individual.
To be diagnosed with panic disorder, one's panic attacks must have been followed by at least one month of steady worry about having more attacks, concern about why the attacks have happened and what they mean (fears of having a serious physical illness or "losing one's mind" are common), or a significant change in behavior brought about by the attacks (many feel the need to avoid certain situations or remove themselves from particular environments).
Panic disorder is diagnosed more often in women than in men and, although the age of onset varies considerably, is most commonly experienced for the first time between late adolescence and the mid-30s. Up to one-half of those diagnosed with panic disorder also have agoraphobia.
Phobias
Defined as exaggerated, involuntary, and irrational fears of particular situations or things, phobias are generally divided into three separate types.  Social phobia is one of them.
Social phobia (social anxiety disorder) Limited specifically to social situations, this particular phobia is typified by extreme fear of meeting new people and of being embarrassed, humiliated, or judged by others. Social phobia appears to be diagnosed equally among the sexes. Usually first appearing in the mid-teens, social phobia sometimes arises from a history of childhood shyness.
A diagnosis of specific or social phobia requires that exposure to the feared object or situation induces anxiety (often in the form of panic attacks), that the individual experiencing the phobia recognizes the irrational nature of their fear, and that the anxiety caused by the phobia becomes disruptive to the individual's lifestyle.