The LDS church (Church of Jesus Christ of Latter-day Saints) has put a lot of effort in distinguishing itself from the FLDS church (Fundamentalist Church of Jesus Christ of Latter-day Saints). The two churches split about 70 years ago over the issue of polygamy. Before the church's split, President Wilford Woodruff issued a manifesto in 1890 stating the his intention to stop promoting polygamy in the U.S. However he and other apostles continued to practice and sanction. Polygamy secretly continued under leadership of presidents Woodruff, Lorenzo Snow and Joseph F. Smith. When congress tried to bar Mormon senator and apostle Reed Smoot from being seated over the issue of polygamy in 1904, the church issued a 2nd manifesto against the practice and disciplined two apostles to demonstrate their commitment to following U.S. dictates. These efforts resulted in the church being able to have an LDS apostle as a senator. Later under Heber J. Grant, the church completely abandoned secret polygamy and excommunicated all practicing LDS polygamists including a group in Short Creek, Utah in 1935, headquarters of today's FLDS church.
Church members had received dual messages from the church leadership for decades. The public voice had been against polygamy, but many knew those outward voices were for public consumption and many knew of others who had privately been sanctioned by the church leadership to continue practicing polygamy. Many held to the revelation received by John Taylor stating that the law of polygamy would never be revoked and that it was a requirement for exaltation.
The culture of conflicting messages resulted in subset of Mormons resolute in keeping the practice of polygamy alive, and the subsequent formation of the FLDS and other Mormon polygamist groups.
Today there are about ten thousand members of the FLDS church. Tens of thousands of other Mormon polygamists are members of other groups. Their beliefs & practices more closely resemble the those of the 19th century LDS church under the leadership of Brigham Young and John Taylor. The LDS church continues it's abandonment of many earlier Mormon practices and beliefs, motivated in part by it's quest for respectability and desire for recognition as a mainstream Christian church. It has vigorously reiterated the distinction between itself and the FLDS reflection of it's former self.