The Executive Office of the President (EOP or sometimes EXOP) consists of the immediate staff of the President of the United States, as well as multiple levels of support staff reporting to the President. The EOP was established by the United States Congress in 1939 after the Brownlow Committee recommended that such a support staff for the President be created.
Since its inception under Franklin Roosevelt, the size and influence of the EOP has increased. The current figures for the EOP are about 1,800 full-time equivalent employees. These employees work in the East Wing and the West Wing of the White House and in the Executive Office Building, an extension of the White House.
"The White House" is shorthand for the compound that houses the EOP.
Cheers,
Scott.