Abbreviation for "The Church of Jesus Christ of Latter-day Saints" or a member of The Church.
Members are formally referred to as "Latter-day Saints." "Saints" as used in the New Testament being any follower of Christ. While it is appropriate to refer to a Latter-day Saint as a "Mormon," it is not appropriate to refer to the Church as the Mormon Church. Other names for the organization that are discouraged are the LDS Church and Church of the Latter-day Saints.
In addition to "The Church of Jesus Christ of Latter-day Saints," "The Church of Jesus Christ" and the "Church" are also encouraged.
"Latter-day Saints" or ("LATTER-DAY SAINTS" when using all caps ) is the appropriate hyphenation and capitalization. Other forms like "Latter-Day Saints" and "Latter Day Saints" are incorrect even though some Mormons use those forms due to a lack of awareness.
It's best to refer to the official style guide - www.mormonnewsroom.org/style-guide.
In fact, "The Church of Jesus Christ of Latter Day Saints" is the name owned and previously used by the "Communities of Christ" and "Fundamentalist Church of Jesus Christ of Latter-Day Saints" is used by a group that practices polygamy. Neither of these organizations has formal ties to the "The Church of Jesus Christ of Latter-day Saints."
The term "Mormon" is also properly used in the "Mormon Tabernacle Choir," Mormon Trail," and "Book of Mormon."
They are members of the LDS faith.
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