The difference between specific phobia and panic disorder is that in specific phobia, you have an intense fear of an object or situation, whereas in panic disorder, you have spontaneous and random panic attacks, and you live in fear of the next panic attack coming.
Certainly, in specific phobia, you can also get panic attacks. But the panic attacks you get in specific phobia are from exposure to your feared object or situation. For instance- if you have a fear of spiders (arachnophobia), then seeing a spider may trigger a panic attack.
The panic attacks in panic disorder occur out of the blue, and can occur at anytime, anywhere, even when resting or sitting down. So you get anticipatory anxiety, where you are on guard for the next panic attack.