Some people use the terms "anxiety attack" and "panic attack" interchangeably. Though similar in some ways, they are actually quite different.
We've all experienced anxiety attacks at one time or another. You're walking down the street alone at night. You begin to hear sounds and fear that someone is following you. Your heart starts racing and you pick up your step. Or you are driving down the road when all of the sudden another car runs a red light, nearly broadsiding you. Your heart starts beating rapidly, you may feel weak or dizzy and you may experience shortness of breath. These are some of the same symptoms that can occur during a panic attack, but the difference is that they are brought on by something real that has just happened to you. There is a reason for your body to have reacted as it did. This is called the body's fight or flight response.
In contrast, a panic attack is something that comes from out of the blue. One minute you are in line at the grocery store, smiling at the cute, little baby making faces at you in the cart ahead, the next minute your heart starts racing, you feel faint and short of breath, and you are convinced that you are having some sort of medical emergency. There is no real threat here to cause these symptoms. (That baby isn't going to jump out of the cart and start attacking you!) Your body and mind are causing these symptoms, and they have nothing to do with any real threat.
Sometimes the lines between anxiety attacks or panic attacks are not that clear. People who have a form of anxiety called Generalized Anxiety Disorder, a constant state of worry and anxiety, can start having panic attacks out of the blue. Those with Panic Disorder can start having what is called anticipatory anxiety, which is when you begin worrying that you will have another anxiety or a panic attack if you go someplace where you have experienced an attack before. Giving into this fear is what causes Agoraphobia to develop, and soon you begin fearing and avoiding more and more places, until your world becomes quite small.