After Smith was killed, the membership of the Church of Jesus Christ of Latter Day Saints fell into confusion and disorganization over the question of succession. Several individuals emerged with claims to leadership and the church's presidency. This led to the formation of several small factions. After periods of debate, the majority of the church's members followed Brigham Young, who led them to the Great Basin area (in what is now Utah) as the Church of Jesus Christ of Latter-day Saints (LDS Church). Other leaders included Sidney Rigdon, James J. Strang, Lyman Wight, Alpheus Cutler, William Smith, and David Whitmer. In the aftermath of this disorganization of the church, the term "Mormon" gradually came to be used primarily in reference to those persons who followed Young and were members of the LDS Church. The remaining individuals—who still considered themselves part of Smith's original church—remained; many who were in scattered congregations throughout the American Midwest joined other factions. Others began forming themselves into a "reorganized" Church of Jesus Christ of Latter Day Saints.
After Smith's death, some Latter Day Saints believed that Smith had designated his eldest son, Joseph Smith III, as his successor; some of these individuals waited for young Joseph to take up his father's mantle. However, Smith III was only 11 years old at the time of his father's death; his mother, Emma Hale Smith, and their family remained in Nauvoo rather than moving to join any of the departing groups.
In the 1850s, groups of Midwestern Latter Day Saints who were unaffiliated with other Latter Day Saint factions began to come together. Leaders, including Jason W. Briggs and Zenas H. Gurley, Sr., began to call for the creation of a "New Organization" of the Latter Day Saint movement. They invited Smith III to lead their New Organization; he accepted only after he believed he received a personal spiritual confirmation that this was the appropriate course of action.
At a conference on April 6, 1860, at Amboy, Illinois, Smith III formally accepted the leadership of what was then known as the Church of Jesus Christ of Latter Day Saints. William Marks, former stake president of Nauvoo, served as Smith III's counselor in the reorganized First Presidency. The word "Reorganized" was added to the church's official name in 1872, mostly as a means of distinguishing it from the larger LDS Church, which at that time was involved in controversy with the U.S. government over its doctrine of plural marriage. The Reorganized Church of Jesus Christ of Latter Day Saints was often abbreviated "RLDS Church".
Speaking of organized religions without a leg to stand on.
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...and in all cases consider the source.