Semantic Chickens
Military
Detainee
Prisoner
Coined
Military and government usage; became the standard term after 2001
Protects
The government from the protections that attach to the word "prisoner."

A prisoner of war has rights under the Geneva Conventions, with a name, a status, and a list of things that may not be done to them. A detainee has whatever the detaining power says they have. The word was adopted because the rights attach to the noun, and a new noun has no rights attached.

“Detain” is a soft verb. One is detained at the airport, detained by a phone call. It suggests delay rather than confinement, a pause rather than a cell. Apply it to a person held for years without charge and the word does a great deal of work, all of it in the direction of making the thing sound temporary and procedural.

This is the Department of Defense pattern in miniature, and the one Mamet would recognize at once. The name was not changed to describe the practice more accurately. It was changed so that the old description, with its obligations, would no longer apply.