In Europe, "minister" is used to refer to a high-level official in government -- for example, the prime minister, foreign minister, minister of transportation, or minister of a particular department of government. In the United States "minister" is used to refer to the leader of a church, particularly a Protestant church. The term used for this purpose in Europe is "clergyman" or "clergywoman" or "clergyperson."
Some people think that having women as members of the clergy is a relatively recent development. But the term "clergywoman" actually dates back to as early as 1673, only 100 years later than "clergyman," which dates back to 1577. The use of "clergyperson" came into use in about 1976, on the coattails of the emphasis to use exact gender.
In the United States there are five primary titles people use in referring to the clergy or minister or leader of their particular church or synagogue, depending upon the denomination or the geographic location of the congregation. Each is a legitimate title because each describes an aspect of the clergyperson's job. Let's take a look at each of them. I use the King James Version when referring to the Bible.
It has not been my purpose to formulate detailed job-descriptions for clergypersons, but, instead, to call attention to five "umbrella" responsibilities under which daily details fall. I have intentionally omitted discussing "Reverend" and "Father," titles often used when directly addressing Protestant or Roman Catholic members of the clergy; they are titles of respect and do not exemplify aspects of the clergyperson's responsibilities.