What is it called when a country controls itself and other countries?

When a country controls itself and other countries, it is often referred to as an empire or Imperialism. In this context, imperialism describes the policy or practice of extending a nation's authority by territorial acquisition or by establishing economic and political dominance over other nations. This can manifest through colonization, military conquest, or economic coercion. Such control can lead to significant influence over the governed territories' resources, culture, and governance.