The most common terms include: minister, preacher, pastor, and priest (priest is usually used in reference to Catholic "pastors").
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A Christian religious hermit is called an eremite.
No, a minister is a broader term that can refer to any ordained religious leader, while a pastor specifically refers to a leader of a Christian congregation.
A minister typically lives in a rectory or parsonage, which is a designated housing provided by a church or religious organization for its minister.
A female minister is commonly referred to simply as a "minister." In some contexts, she may also be called a "female minister" or "woman minister" to specify her gender. The title may vary depending on the religious or governmental context, but the term "minister" itself is gender-neutral.
A minister's house is typically called a parsonage or a manse. It is provided by a church or religious organization for the minister to live in while serving the congregation.
Syed Hamid Saeed Kazmi, Minister for Religious Affairs Ms. Shagufta Jumani, Minister of State for Religious Affairs
Hsan Hsint is the Minister of Religious Affairs for Burma.
Mukhtar Gomaa is the Minister of Religious Endowments for Egypt.
Suryadharma Ali is the Minister of Religious Affairs for Indonesia.
Naftali Bennett is the Minister of Religious Services for Israel.
Xavier Bettel is the Minister of Religious Affairs for Luxembourg.