An Empire is a place where you don't get to chose a ruler. A republic is where you get to vote on a ruler.
A republic is political order whose head of state is not a monarch and in modern times is usually a president.
A empire is political unit having an extensive territory or comprising a number of territories or nations and ruled by a single supreme authority
An Empire is ruled by a emperor, and a Republic is ruled by people we elect to make decisions for us...
A republic is ruled by the people, a empire is ruled by an emperor.