FLDS is a splinter group of the mainstream LDS church. The FLDS splintered off when the church disavowed polygamy in the 1890's. 
 
FLDS and LDS are nothing alike in culture, and only somewhat similar in doctrine. LDS live among the general population of the world, while FLDS live in compounds or small, insular communities. 
 
Theologically, LDS have chosen to focus on the mainstream commonalities between Mormonism and Christianity, while FLDS have tended to focus on the differences and oddities between the two. 
 
I lived near FLDS for much of my life. They believe in their faith, but are very distrusting of others and often distort the truth to protect their way of life and beliefs.