Both of these cases dealt with state-approved reading of Bible passages before classes in public schools. Schempp was brought to trial by a relgious family who had contacted the ACLU. Murray was brought to trial by an atheist: Madalyn Murray (later O'Hair), who was working on behalf of her sons, William and Garth. Murray challenged a Baltimore statute that provided for the "reading, without comment, of a chapter of the Holy Bible and/or of the Lord's Prayer" before the start of classes. The Court ruled 8-1 against requiring the recitation of Bible verses and the Lord's Prayer.
Read Article: Abington School District v. Schempp & Murray v. Curlett (1963)
Of course William Murray has for years agitated for the other side.
I recently read a biography of O’Hair which included her awful murder in the 1990s as well as the events leading up to and including the U.S. Supreme Court case you mentioned. Fascinating stuff (although the murder and subsequent investigation was quite grisly).