In 1861 the train would have traveled on a number of different short line railroads to get from New York to Washington (the Philadelphia & Trenton; the Philadelphia, Wilmington & Baltimore; the Baltimore and Washington, etc.); the Philadelphia, Washington & Baltimore Railroad was not formed until 1902 and it was still in existence (on paper) until 1976. Obviously the filmmakers kept the name consistent to provide continuity and to avoid having to repaint the engine and cars after every few shots.
The first director attached to this subject, several years before the film was finally made, was Joseph Losey. He had planned to cast Lena Horne in the role finally played by Ruby Dee - originally planned as a much larger part.
The names of all the stations mentioned in the film on the line as the train travels south out of New York would be familiar to a traveler on the modern Northeast Corridor as they are still used by Amtrak, except for Darby Junction which is a now a station on the Southeast Pennsylvania Transportation Authority's Wilmington/Newark regional rail line. Their placement in the film is geographically accurate - Darby Junction would have been the first place the train could have stopped south of Philadelphia.