The correct answer to this open question is the following.
The definition of "one nation controls the government or economy of another nation" is "Imperialism."
Imperialist nations have a foreign policy that conquers other territories and forces the other nations to subjugate to the economic and political interests of the powerful nation. The powerful nation brings many territories under its control. One good example should be the imperialistic foreign policy of Greta Britain in Africa, where the English controlled many countries such as Egypt and South Africa.