No- agoraphobia is not a social phobia or a specific phobia. Agoraphobia is a fear of places where escape may be difficult or help may not be available in the event of you having a panic attack or other incapacitating or embarrassing symptoms (fear of falling, fear of incontinence, etc.). Furthermore, agoraphobia diagnosis requires the presence of at least two feared situations, such as fear of open spaces (parking lots, bridges), fear of enclosed spaces (theatre, shops), fear of public transportation (plane, train, bus, car), fear leaving your home alone, or fear of lines or crowds (APA, 2013).
This contrasts with social phobia, also known as social anxiety disorder. The primary fear in social phobia is the fear of being embarrassed, or the fear of social scrutiny. With specific phobia the fear is only limited to one situation, for instance you may have an intense fear of being on a bridge, but have no other situational fears. In agoraphobia, the fear is different- you fear being out in places as you are afraid that help may not be available or escape may be difficult if you have a panic attack there. For example someone with agoraphobia might have fear of being on a bridge and fear of flying because going on either of them would make escape impossible if you were to have a panic attack. With agoraphobia, you have at least two feared situations, whereas with specific phobia you only have one.
The distinction between agoraphobia and specific and social phobia is important, as agoraphobia is associated with severe impairment and severe disability, given that people with agoraphobia are not able to leave their home and not able to function at work or school. People with agoraphobia also may have impaired relationships and poor self-care skills. People with social phobia may avoid social situations, but they are still, for the most part, able to leave their homes and function at work or at school, but they just avoid social contact, or endure it with much discomfort. With specific phobia they just avoid a very specific situation, and can function with other areas of their lives.
The good news is that help is available for agoraphobia and other phobias. CBT, or cognitive behavioral therapy, is an effective and safe treatment. For cases where CBT is not helpful or for severe anxiety symptoms, then medication can be considered. For more information and help on agoraphobia, specific phobia, and social phobia (social anxiety disorder), please take a look at the articles on Anxiety Boss.