"Stunned" can be used when someone is surprised or caught off guard. It also can be used when someone is scared. "Scared stiff" would be used when someone is really REALLY scared. Sometimes people get so scared to the point that their body stiffens. That's where the saying "scared stiff" comes from.

Scared stiff means really afraid. Stunned means amazed or taken back.

If you are "scared stiff", it usually implies you saw or experience something that really made you scared, to the point where you can't move. If you are "stunned", this can take on several meanings. You could be scared, shocked, speechless from witnessing something that makes you uncomfortable, not just frightening.