How and why did foreign policymakers handle Germany and Japan differently in the years immediately following World War II? What were the specific comparisons between postwar plans for both states?

This is a very interesting question, and a very important one, given the lasting impact of the post-War era in shaping the twentieth century. I would begin, first of all, by noting that probably one of the most striking differences between the cases of Germany and Japan lay in the nature of the occupation: Germany, ultimately, faced a two-pronged attack, with the Russians sweeping in from one side, and the Allies from the other. This resulted in a divided occupation, the result of which was a divided Germany in the post-war era. The Soviet Union would control East Germany (and turn it into one of its satellite states), as opposed to West Germany, which would itself be drawn into the United States's sphere of influence. Japan, on the other hand, was able to avoid this kind of political division in its own post-war future.
Ultimately, any discussion of Post-World War II politics has to factor in the role of the Cold War and the degree to which US-USSR rivalries ultimately took primary focus in the political and strategic decision making during the time period in question. In both West Germany and Japan, the US government had an interest in creating a counterweight against Soviet influence in Eastern Europe and East Asia, respectively.
With that in mind, we do see similarities between Japan and West Germany. Both countries were ultimately rebuilt to serve as bulwarks against the further spread of communist influence. Both West Germany and Japan were established as democratic governments, according to democratic principles. In addition, we should note that the United States enacted a policy of economic rebuilding in both countries. The US recognized that economic turmoil had a role in promoting communist ideals, and it spent considerable effort assisting the economic recoveries of both Japan and West Germany after World War II, with the interest of increasing stability so as make each country more resistant against communism. This policy would have significant economic effects moving forwards.