They are similar, yet different. They are similar in that both are phobias, which are fears of some anxiety-provoking stimulus. They are different in that specific phobia involves intense fear of a specific object or situation, while social phobia involves intense fear of social scrutiny by others (or fear of performing in front of others due to the possibility of embarrassment).
Examples of specific phobia include arachnophobia (fear of spiders), fear of heights, and fear of flying. Examples of social phobia (social anxiety or performance anxiety) include stage fright, dating anxiety, and test anxiety- or just plain social phobia (also known as social anxiety disorder).
