Minister has more than one meaning. In government, a minister is a cabinet level advisor to a head of state, generally with a specific area of focus. The term is used primarily in countries using the British Westminster system of government; those using the American system generally call the cabinet head of a department "Secretary".
In Christianity, a minister is a religious leader, usually one who conducts corporate worship, preaches the Good News, and administers the sacraments or ordinances of the church. Christ is recorded in the New Testament as having called his twelve Apostles and giving them the oversight of his church after his departure from Earth. Modern ministers are believed to be carrying on that responsibility within local Christian churches. In most settings it is synonymous with pastor.
Protestants are more likely to refer to their clergy by the term than are Catholics. In Catholicism, a priest is indeed a minister but the word is not normally used as a description of his role. Usually, it is used with the head of a school, in a department, or for laypersons who have been given some limited sacramental function, for example, "eucharistic ministers" who are charged with bringing Communion to shut-ins.