WingCommander: Growing up in the 80's thru 2000 it was always "The New System of Things."
Same here, I always heard it referred to as "the new system" (in Spanish, El Nuevo Sistema). I don't recall ever hearing it referred to as a new order or new world order. When Bush made reference to "a new world order," our JW ears perked up because it sounded a bit like the new system. We just saw it as yet another confirmation that The End was Just Around The Corner.
Narrator: The end was not just around the corner.