Yes, the LCMS Explanation of LSC is rather confusing. The first part is Luther's Small Catechism which is part of the Book of Concord, but the second part is really just a synod training aid.

The LCMS, WELS, and ELS are the largest American synods that hold an unconditional subscription to the 1580 Book of Concord. However, these synods (particularly the LCMS) are experiencing great pressure to ignore or deviate from the Confessions. The ELCA is completely apostate from the symbols although they still list them at their website.