From Latin "Imperium" - lordship, command area. See Rome

The empire can be considered an outgrowth of military conquest. It contrasts with the Federation, a voluntary association. As a conquest it depends on orders being passed from the center. The British empire was a result of conquest and settlement. Its settlement countries remained associated voluntarily; its conquests have become independent.

Orders are passed down from the center to the periphery.

Celtic Ireland is sometimes considered a federation where power was passed upwards to the High King. It was conquered by the Normans who practiced feudalism where the power is that of an empire.