What are they?
A mars light is a forward light meant to get your attention. Typically, they were held by a rotating mechanism that was akin to waving a flashlight around.
Ditch lights do exactly what their names says, they light the ditches. They originated in Canada and have since been adopted in the States. In Canada, they are usually solid all the time, where in the States they will flash alternately when approaching grade crossings.
Usage depends on Railroad and Era.
David B