The difference between green and white teas is mainly due to the different methods of oxidation in processing. With green tea, the oxidation is halted at a very early stage after being initially withered, a step often called kill-green, or fixing. After that, the leaves are dried.
White teas, on the other hand, don't undergo this fixing step; they are either withered for several days, then dried, or withered until dry, usually with no rolling or shaping of the leaves. This method causes the enzymes responsible for oxidation to be mostly deactivated, though many stress that oxidation continues, albeit at a very slow rate, throughout the useable life of the finished tea.
It's not accurate to say that white teas are altogether less potent in either taste or caffeine content than their green counterparts. The best white teas are intensely aromatic and flavorful, and many are highly stimulating.