Do both monetary policy and fiscal policy shift the aggregate demand curve?

Yes. An expansionary fiscal policy, or more optimistic growth expectations in the private sector will shift the aggregate demand (AD) curve upwards. The position of the AD curve is also affected by the central bank's inflation target, if the target falls, the AD curve will shift downwards. Monetary policy influences the slope of the AD curve as well as the position. If the central bank put strong emphasis on fighting inflation and little emphasis on stabilizing output, the AD curve will be flatter. The other way around will yield the opposite result.