In both cases, the presidents are using the powers as leader of the military to accomplish aims for public safety.
President Roosevelt's Executive Order No. 9066 was issued in response to fears of espionage and sabotage during World War II, arising from the societal change brought about by the war mobilization and the Japanese attack on Pearl Harbor. This executive order authorized military commanders to create exclusion zones from which Japanese Americans were forcibly removed, leading to their internment. The rationale was the perceived need to protect national security, reflecting widespread societal fears and prejudices against Japanese Americans.
In contrast, President Eisenhower's Executive Order No. 3204 addressed a different societal change: the desegregation of public schools following the Supreme Court's Brown v. Board of Education decision, which deemed racial segregation unconstitutional. Eisenhower's order aimed to enforce the court's ruling in response to violent resistance and obstruction from segregationists in Little Rock, Arkansas. By deploying federal troops to ensure that African American students could safely attend Central High School, Eisenhower used his military authority to uphold civil rights and maintain public order amidst societal tensions regarding race and equality.
In summary, both presidents exercised their military powers in response to concerns about public safety; however, they each confronted different societal changes—war-related fears in Roosevelt's case, and civil rights issues in Eisenhower's.