Demand- and supply-side economics are both based on the general faith in markets. In both cases, the differing views suggest that markets are essentially rational allocators of resources and rewards, but the engine of that market is the area of difference. These two schools of economics seek the alleviation of unemployment and the most rational uses of government to achieve the ends of rational and justifiable rewards.
Governments have a fairly limited arsenal of policy weapons to use in the economy. Taxation and regulation are always the two major sources of government intervention. In addition to those, governments can buy industry, promote public works, increase welfare and unemployment payments, start wars, restrict imports and mobilize labor. These government weapons in the economy are seen very differently by demand- and supply-side economists.
Supply side, as the name suggests, takes the producers and investors of wealth as the main engine of economic development. The basic argument is that the producers and investors need a set of incentives to promote investment and innovation. This set of incentives requires the state -- seen as an unproductive and parasitical entity -- to reduce taxes on those groups and classes most likely to invest their money wisely in production and innovation. Therefore, taxes should be low, budgets should be balanced, regulation kept at a minimum and international trade should be kept free.
The demand side takes most of its theoretical work from the British economist John Maynard Keynes. He held that the real engine of economic development comes at the level of the consumer. Therefore, governments should be deeply involved in the economy. If the consumer -- and therefore, demand -- is the engine of economic growth, then the state should do all in its power to increase the spending power of the average person. This, in turn, requires that the state engage in public works and increase all forms of entitlements. Full employment is the goal of the demand-side economist, and it matters not where the source of that employment is. All that matters is that consumers continue to buy products and services, and keep the economy spinning.
States and Markets
These two schools of thought, while believing in the market mechanism, view the market differently. The supply-side advocate sees markets as closed, self-contained units. They are inherently rational since consumer demand is quickly translated into prices that then send signals to producers to make more of an item. Demand-side advocates hold that there is no real reason to believe that cutting taxes will mean that producers and investors will rationally invest their saved money. The differing views on government policy relative to markets are based on the two schools' views on human rationality. For the supply-side advocate, low taxes and minimal regulation will lead to rational outcomes, since everyone wants to profit. The demand-side will hold that the market does not guarantee full employment and therefore is self-defeating, since the unemployed cannot buy anything. The investor is just as likely to invest in non-productive things as in productive things. Policy matters here because the government can "fill in" where the market fails.