Minister vs. Secretary

Solution 1:

The system of nomenclature is unique from government to government, and the terminology of the United States government was established with the expressed purpose of differentiating from the monarchial system in England when Independence was gained. In the United States the Federal Government is divided into three branches:

1. Legislative Branch

The United States Congress is the legislative branch of the federal government. It is bicameral, comprising the House of Representatives and the Senate.

Wikipedia.org

• A members of The House of Representatives is called congressman or congresswoman:

congressman

noun (plural congressmen)

A member of Congress, especially a member of the US House of Representatives:

congresswoman

noun (plural congresswomen)

A female member of Congress, especially a female member of the US House of Representatives:

ODO

• A member of the Senate is called senator:

noun

1 A member of a senate, in particular a member of the US Senate:

ODO

2. Executive Branch

The executive power in the federal government is vested in the President of the United States, although power is often delegated to the Cabinet members and other officials.

Wikipedia.org

• The Chief Executive Officer is called president:

noun

1 The elected head of a republican state:

ODO

• The President's replacement is called called vice president:

noun

An official or executive ranking below and deputizing for a president:

ODO

• The President appoints a cabinet of unelected officials, including fifteen people who oversee the details of federal executive departments.
• With the exception of the Attorney General, each head of a federal executive department is called Secretary of [Specific Name of Department]:

1.3 An official in charge of a US government department.

• Each federal executive department is organized with Bureaus, Agencies and Administrations, as well as numerous other smaller subsections of executive responsibility.
• The leaders of these subsections are predominantly called director:

noun

1 A person who is in charge of an activity, department, or organization:

ODO

3. Judicial Branch

The Judiciary explains and applies the laws. This branch does this by hearing and eventually making decisions on various legal cases.

Wikipedia.org

• Each member of the judiciary is called justice:

2 A judge or magistrate, in particular a judge of the Supreme Court of a country or state.

ODO

• The presiding member of the Supreme Court is called the Chief Justice:

1.1 (Chief Justice of the United States) (The formal title of) the chief justice of the US Supreme Court.

ODO