For me, an anxiety attack if when you think too much about something. Like when you're driving and you keep thinking you are going to have a heart attack, eventually, anxiety builds up to the point where you give yourself an anxiety attack.
A panic attacks comes out of no where. Like, you're staring out the window and all of a sudden, you can't breath and you feel like it's the end of the world and you are going to die right then and there.
Basically, an anxiety attack is self inflected. Caused by too much worrying, over thinking, etc.