Tool and Die - Forming dies
Forming dies are typically made by tool and die makers and put into production after mounting into a press. The die is a metal block that is used for forming materials like sheet metal and plastic. For the vacuum forming of plastic sheet only a single form is used, typically to form transparent plastic containers (called blister packs) for merchandise. Vacuum forming is considered a simple molding thermoforming process but uses the same principles as die forming.
Compound dies are simpler dies, often used when the quantities of parts produced don't warrant the expense of a progressive die. Compound dies can be large or small to handle varying thicknesses of metal--big and heavy duty for thick gauge metal; smaller for components.
There is some overlap in die descriptions: there are hybrid compound dies, which can exert force on the metal in different directions, and complex compound dies, which use nitrogen cylinders.