the insurrection act of 1807 was used many times. It is an exemption of Posse Commitatus that allows the Federal Gov to get around the whole not using troops against the citizenry thing. Lincoln used it once to fight the Democrats before the Civil war and Eisenhower and Kennedy used it against racist democrats fighting desegregation. It was used during the Indian was and multiple riots over the years as well. Martial law is a state or local governance level event. The Insurrection act is a federal level event. That is basically the difference.