A group of countries ruled over by a single monarch or ruling power. An empire doesn't need an emperor.
Colony
A country or area under the control of another country.
Imperialism
A policy of extending a country's power through colonisation, use of military force, or other means.
Colonisation
The action of taking control of an area/country and its people.
Colonialism
When a powerful country (e.g. Britain) directly controls less powerful countries and uses its resources to increase its own power and wealth.
The first parts of the British Empire were North America and the smaller islands of the Caribbean and the establishment of joint-stock companies, most notably the East India Company
The second part of the British empire included Egypt, Kenya, Nigeria and large areas of southern Africa