Parts of the Bureaucracy
There are 15 cabinet departments, including the Department of Defense, and the Department of Health and Human Services, and they are all led by a secretary, except for the Department of Justice, which is headed by the Attorney General. They all focus on a specific area, like education, labor, or commerce.
Independent Regulatory Commissions
An independent regulatory commission is an agency that is responsible for making and enforcing rules designed to protect the public interest for some sector of the economy.
They are headed by a small commission of 5 to 10 members appointed by the president and confirmed by the Senate. It's very difficult to fire a member of a federal regulatory commission. The last time that happened was during FDR's presidency, and that went up to the Supreme Court, which said the president can't fire a member without "just cause".
FCC (Federal Communications Commission)- Responsible for regulating TV and radio stations, along with the Internet, and cable.
NLRB (National Labor Relations Board)- Regulates labor-management relations
FTC (Federal Trade Commission)- Regulates business practices and monopolies
SEC (Securities and Exchange Commission)- Police the stock market
A government corporation does an action that a private corporation would do, but they are much cheaper.
TVA (Tennessee Valley Authority)- This was established in 1933 as part of the New Deal, and they built railroads, provided electricity to millions, and controlled floods.
USPS (United States Postal Service)- Sends mail to millions
Amtrak- Railroad passenger service
Independent Executive Agencies
Those are essentially the rest of the government, so anything that doesn't fit into the first three categories.
NSF (National Science Foundation)- Supports scientific research
NASA (National Aeronautics and Space Administration)- Builds rockets and sends people to space