Americans used a box wagon with four wheels of the same size. The German wagons have two different sized wheels and and angular rear cargo area. The Americans also used mules as much as horses. The Germans generally used horses but used other animals as needed.
Us the Imex wagons for Americans, they already make a chuck wagon.
I know nothing about wagons prior to WWI in Europe, or AWI in North America.
As for a command wagon, the WWII Germans did have Enigma machines in them. Just Google WWII German Wagons, Image and you will find lots of them.