Most sources refer to the civil rights organization Martin Luther King led as the Southern Christian Leadership Conference (SCLC), but some refer to it as the Southern Baptist Leadership Conference (SBLC).
Mr. Wyatt, a member of the Baptist Ministers Conference of Greater New York, a chief sponsor of the observances, urged citizens to take a day off from work “in memory of this great man,” or to forward a day's pay to the Southern Baptist Leadership Conference in Atlanta. New York Times Jan 12, 1972.
and in an advertisement offering a poster from The Poor People's Campaign,
The iconic poster for the Poor People's Campaign. A photo of MLK holding this poster was distributed to newspapers in 1968 with the caption "Civil Rights Leader Rev. Dr. Martin Luther King, Jr., president of the Southern Baptist Leadership Conference (SCLC), displays the poster to be used during his Poor People's Campaign this spring and summer, March 4, 1968..." Poor People's Campaign poster
What was the history behind there being two names? Ralph Abernathy, with whom King founded the group, was, like King, a Baptist minister, so it might make sense that "SBLC" was the original name, but changed later to be more inclusive?