Monetary policy takes medium run time to take effect. Why study it in short run?
In an IS-LM model, expansionary monetary policy increases output and decreases the interest rate. Expansionary fiscal policy increases output and increases the interest rate, so the two types of policies are not equivalent.

Furthermore, monetary policy does not work in the long-run. See an AS-AD model for more details on that. The only reason monetary policy actually works, is because of the fixed prices and their slowly changing (increase) in the medium run. Otherwise inflation would rise immediately in response thereby making monetary policy not have any effect on real GDP.

To really get to the medium run you have to understand the short run first. Effects observed in the actual economy often are not as quick as in our models and take time. I wouldn't consider 4-8 quarters the medium run.

Hope this helps.