Why did the CIA have the same plane as Pussy Galore?

Basically, in the end when Bond gets on the plane it turns out that Goldfinger and Pussy Galore are on it, and that Goldfinger has tied up the real pilots, and they are left in the hanger.

However, this looks exactly like the same plane that Bond was held hostage on earlier by Goldfinger.

So why would the pilots who were taken hostage, have been operating the same plane, unless it's not the same plane?

Because the filmmakers used the same set to save bucks, duh.

This is a rare case of the novel being more outlandish than the film.

In the book, Goldfinger hijacks a BOAC Constellation, which was a giant piston-engine airliner that was fast approaching obsolescence even in 1957 when the novel was written. By the time the film appeared three years later, its BOAC equivalent was the Boing 707. However, the hijacking of a commercial flight makes no sense (Fleming's ideas were often nonsensical), so Eon gave Auric his own Lockheed Jetstar, which was the world's first bizjet. While it makes no narrative sense that the authorities didn't impound it, I imagine Lockheed allowed Eon access to one for promotional reasons, which would explain its two appearances. As CJB says, one less set to build as well.

Okay thanks.  But inside the airplane hanger, you see the pilots tied up who were suppose to be the people picking up Bond in the plane right?  The same people that Felix talked to when he said 'liquor for three', right?

So why were these pilots planning on flying Goldfinger's plane to pick up Bond?  Does it make any sense for the President inviting Bond to the white house, but the pilots that the President sends to pick him up, were going to choose to fly the plane of the terrorists' who almost nuked Fort Knox hours earlier?

Lyndon Johnson was known for barking orders while sitting on the crapper, so obviously something was lost in translation before they made Bond's travel arrangements.