What is it called when many countries are governed by 1 authority?

When many countries are governed by one authority, it is often referred to as an empire or a federation, depending on the context. An empire typically involves a central power exerting control over diverse territories and peoples, while a federation consists of multiple states or regions that unite under a central government while retaining some degree of autonomy. In modern contexts, this could also refer to supranational organizations, like the European Union, that facilitate governance across member countries.