I am currently formulating a paper on the evolution of strategic bombing, and my thesis is that the Allied experience of German terror bombing during WWI shaped the theories of Douhet, Mitchell, Seversky, and others. Lacking a similar experience, the Germans focused on a tactical air force as a core component of the Blitzkrieg and did not invest in strategic bombing due to it not being a task expected of the Luftwaffe until after the war had begun.
In addition to MeneMeneTekelUpharsi's excellent answer, it's also important to observe Williamson Murray's rather trenchant take on strategic bombing and the too sharp line distinguishing between tactical and strategic airpower:
For the purposes of [Strategy for Defeat: The Luftwaffe 1933-1945], the use of the term "strategic" bombing is enclosed within quotation marks, as this author believes that the use of the word by airpower enthusiasts to connote a particular form of bombing distorts the classical meaning of the word. The difficulty in which the misuse of this word had led historians might be best characterized by the following question: In May 1940, given Germany's military situation, what was the best strategic use to which the Luftwaffe could be put: supporting the army's drive to the Channel and the crushing of French and British landpower, or attacking French factories and cities? The answer is clear in a classical sense. Within the existing definitions of "strategic" and "tactical" bombing, it is not so clear.
Williamson also notes that strategic bombing, despite Douhet's promises, is a form of attrition warfare, requiring a force structure which German production could not supply. Later war developments in German bombers tried to sidestep this numeric limitation by investing in what would later be termed force-multipliers such as the refinement of the schnellbomber concept or the development of new weapons like guided munitions (standoff antiship missiles/glide bombs or the V-1 cruise missile, which traded accuracy for eliminating the risk of a plane being lost to air defenses). The results of this investment were mixed and often highly contingent upon wartime imperatives. Quite simply put, the German economy could not simultaneously conduct a major land war and devote the resources needed to create an equivalent of the 8th Air Force. Adam Tooze's The Wages of Destruction: The Making and Breaking of the Nazi Economy notes that German productive capacity was operating at the breaking point for much of the war. In some ways, the RLM's force recognized these limitations as the wartime generation of bomber designs were to perform a bewildering variety of tasks (anti-ship, intruder, classical level bombing, dive bombing, etc.). A heavy four-engined bomber force devoted exclusively to dumping tonnage upon enemy industrial areas was something exceeded the reach of the German economy.
I wrote a response to a similar question here a while ago.