There are two main similarities between fiscal policy and monetary policy. The first of these has to do with the goals of these policies. In both cases, the goal is to keep the economy growing at a steady pace. In both cases, the goal is to make sure that there is economic growth (growing Real Gross Domestic Product and low unemployment) while simultaneously making sure that inflation does not become a problem. The second similarity is in one part of the mechanism for regulating the economy. Both types of policy are meant to affect aggregate demand. Both types of policy will try to increase aggregate demand when times are bad and slow its growth when times are good. The policies are not really able to affect aggregate supply.
There are also two main differences. First, the two kinds of policies are implemented by different groups. Fiscal policy is the domain of Congress and the President as it is set through laws. Monetary policy is devised and carried out by the Federal Reserve, which is independent and unelected. The mechanisms are also different to some degree. Fiscal policy uses changes in taxes and spending to affect aggregate demand. By contrast, monetary policy uses such things as interest rate changes and open market operations to affect aggregate demand.
Thus, the two sorts of policies are conducted by different groups in different ways, but both are meant to achieve stable growth by manipulating aggregate demand.