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Monetarist policies are based on the exchange equation,MV=PY. V is assumed to be constant. An increase in money supply which is not associated with the growth of real GDP,will be the cause of inflation. But later it has found that the monetarist policy won't work in a situation,called stagflation. This was because V has been increased with inflation. So the best suggestion, is to increase money supply only regularly based on the increase in real GDP.To go further, it has found that inflation will not decrease unemployment in the long run.

Neo-classical policies are based on the free market principle. If wage and price are flexible, the price will adjust with an increase in demand. The nominal wage will be adjusted upward,so that the real wage will come back to the equilibrium.But it has found further that even I=S, it has not meant that the economy will be in equilibrium in the long run. The capacity will increase with GDP, so that a continued increase in investment is need to bring the economy on track.It is also important that there is an improvement of technology with the time.The golden rule is that the growth of GDP must be equal the growth of capital and the labor.

They aren't that far apart.

Usually people discuss the differences between the Monetarists and the Keynesians.

Monetarists believe that the money supply has sufficient leverage to supply all of the stimulus an economy needs in times of economic distress. And it acts in a quicker, more precises and less politicized fashion than fiscal policy.

Furthermore, Monetarists believe that an arbitrary or capricious policy will create economic uncertainty and distress. The central bank should be predictable in its monetary policies, and ideally be rules based.

The neo-classicists for the most part agree with the monetarists. Fiscal policy should not be used to stimulate the economy. However, they can be a bit dubious of the central banks ability to debase the money through inflation. Many Neoclassicists believe that the money supply should tie the value of money to a "hard asset" such as gold. At the extreme end they may want to eliminate the Fed.