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National Flag
A traditional design is a pole which carries one large national flag with an additional small,
Olympics
At international events like the Olympics, World Cup and Commonwealth Games, a nation's own Olympic committee may also fly its own national flags,
Flagpole
The military camp flagpole is a tall metal pole with a large flag on top, which is usually not lowered at night but instead left flying every day while they sleep.
Headquarters
The staff in a military or civilian headquarters, displays the headquarters' flag (also called a headquarters flag or command flag), from which is flown the national flag.
Building
In this case, there's a distinction between the 'flagpole', which is fixed in position and an integral part of headquarters, and the 'flagstaff', which is detached from the building,