Panzer corps were created throughout the war, and existed in the Army, the Waffen-SS and even the Luftwaffe.
Later in the war it was possible to find panzer corps that consisted solely of infantry divisions.
Panzer groups were named (i.e. not designated with numbers) during the campaigns in Poland, France, and Greece, they were not used at all in Norway and Denmark in 1940, and numbered 1-4 during the first half year of the war against the Soviet Union.
In the last case, a panzer group normally consisted of two or three motorized corps.
The motorized corps served as the tactical command element in the command structure, with the individual divisions serving as tactical combat elements.