A superficial explanation of the fundamental difference between supply-side and demand-side economic stimulus theory

Supply-siders believe that economic productivity is driven from the top: that capitalists will take their new tax breaks (or whatever the stimulus mechanism is), invest in expanding their businesses and increasing production. Then, because this generally requires employing more people, unemployment will drop, the middle class will expand, and demand will be increased indirectly. The problem here is that the capitalists will often actually use their increased income to increase their personal spending rather than invest in expanding their firms, ie, the luxury yacht market will do great, but that's about it.

Demand-siders believe that economic productivity is driven from the bottom (or, more accurately, the middle): that the poor and workers will take their new government aid (or whtever the stimulus mechanism is), buy more food, more clothes, better housing, and generally creating more demand. Then, because this generally requires producing more stuff, businesses will have an indirect incentive to expand, and unemployment will drop. The problem here is that putting more money into the hands of consumers causes inflation.