I often get frustrated when people talk about anxiety attacks and panic attacks as if they're the same thing. Panic attacks come on suddenly and involve intense and often overwhelming fear, sometimes due to a phobia, for example. They’re accompanied by physical symptoms, such as a racing heartbeat, shortness of breath, or nausea.
Anxiety attacks generally build up over a period of time and is related to worry about some a real or perceived danger. If the anxiety builds up and reaches a level where it becomes overwhelming, it may feel like an "attack."
Therefore I think that you can have both at the same time. The anxiety builds up over a long time and you have an anxiety attack. What could then happen is a panic attack due to extra sensitivity to irrational fears due to anxiety.
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