The names of government offices in charge of military and defense affairs can vary significantly across different countries, leading to different terminology like "Department of Defense" or "Ministry of National Defense". Both entities share similar functions but are distinguished primarily by their regional or national usage and the administrative traditions of the respective countries. Below, I will provide a detailed overview of these two terms, including their origins, functions, and examples of countries utilizing these designations.

### Department of Defense

#### Overview
The term "Department of Defense" (DoD) is commonly used in countries such as the United States and Australia. This department is a national executive department charged with coordinating and supervising all agencies and functions of the government directly related to national security and the armed forces.

#### History in the United States
In the United States, the Department of Defense was created by the National Security Act of 1947. It merged the Department of War (formerly known as the War Department, established in 1789), which had been responsible for land-based military operations, and the Department of the Navy, which had overseen naval operations. The formation of the DoD was part of a larger reorganization intended to unify the branches of the military under a single department to provide for more efficient coordination during the Cold War.

#### Functions
The DoD is responsible for overseeing all agencies related to the military, including the Army, Navy, Marine Corps, and Air Force. Its functions include ensuring the security of the country, managing military forces, procuring advanced weaponry, conducting military research, and overseeing military intelligence activities.

#### Structure
The Department is headed by the Secretary of Defense, who is a civilian and a member of the cabinet of the President. Below the Secretary, military chiefs and other civilian officials assist in policy formulation and administration.

### Ministry of National Defense

#### Overview
The term "Ministry of National Defense" is commonly used by many countries, including China, France, and South Korea. This designation reflects a bureaucratically styled body that typically belongs to the larger executive branch of the government.

#### History in France
In France, the Ministry of National Defense was established post-World War II, evolving from earlier structures such as the Ministry of War and Ministry of the Navy. The changes were made to merge the management of the army, air force, and navy under a single organizational umbrella, facilitating better coordination and administration.

#### Functions
The Ministry of National Defense is responsible for the administration and operational control of the military forces, defense procurement, military research, and national security policy. Similar to the US DoD, these ministries ensure the preparedness of the military, oversee the defense budget, and implement strategic defense policies.

#### Structure
This ministry is also headed by a civilian Minister of Defense, who is often a senior member of the government. The minister is supported by deputy ministers and military chiefs. The structure typically includes various departments or directorates focusing on different aspects of military and defense operations.

### Regional Usage and Terminology
The choice between the two terms often stems from historical, linguistic, and cultural factors. English-speaking countries with a British historical influence might prefer "Department of Defense," while countries with different lingual inheritances lean towards "Ministry of National Defense." Additionally, the choice may be influenced by political and administrative reforms.

### Summary
Although "Department of Defense" and "Ministry of National Defense" may sound different, they essentially perform similar roles concerning defense administration in their respective countries. Their primary purpose remains the defense of the nation and overseeing military operations, despite their differing nomenclatures.