N.S. stands for New School rather than Old School. The PCUSA split in 1837 into N.S. and O.S.
During the Civil War the Southern churches split off. The N.S. forming in 1857 the USPC. The O.S. forming in 1861 the PC-CSA. In 1865 the USPC and the PC-CSA merged to form the PCUS.
During the Civil War the Northern Churches continued on as O.S. and N.S. and merged in 1870 as the PCUSA.
USA=United States of America
CSA=Confederate States of America
The importance of all this is not just what they believed but that they believed it strongly enough that they were willing to go to the hassle of creating new denominations and each church having to decide which denomination they would associate with. Each denomination had periodic General Assembly meetings and minutes and associated with these minutes were statistical lists showing all the churches in their denomination and where each of their ministers was serving.