Is their difference between a anxiety attack and a panic attack? and can you have anxiety without feeling anxious?

Panic attacks: Anxiety attacks and panic attacks are just two ways to label the same experience. In response to your second question, anxious feelings would generally accompany episodes of anxiety. One can reduce anxiety feelings with a good CBT therapist. Medications can help during episodes, but they do not provide a long term solution. Anxiety attacks are very common and they can be reduced and controlled.