Formal logic deals with apprehension, judgment and reasoning while material logic deals with the evaluation of measurable factors. These two divisions of logic are not considered strictly separate and there is some debate over whether or not they are different in a purely legal sense.
Formal logic proceeds from methods of observation and comprehension. It deals with the evaluation of logical statements and objects and with the tools used to arrive at those evaluations.
Material logic proceeds from assessment of physical and observable quantities. It is considered procedural and very focused on ideas of hardness and softness as they relate to the quality of evidence in either a legal or debate-postulate sense of the word.