White flags (or lights at night) indicate an "extra" or unscheduled train. Extra trains have the lowest priority and depend on train orders to allow them to operate.
Green flags (or lights at night) indicate that a additional (second, etc) section of a scheduled train is following and has the same operating rights as the train displaying the markers (flags or lights). Some railroads scheduled not only first class passenger trains, but also second class (freight, etc.) trains. The final section of a scheduled train would not display any markers. So, if you ran three additional sections of a scheduled train the first, second, and third sections to depart would display green and the fourth or last section would not display.
Brian Norden