That's exactly what I just said.
Xbox 360S is an indentifier for the manufacturer, not for the customer.
Then why is it on the box as part of the contents?! It's always been called the Xbox 360 S, in order to differentiate it from the 360s of old. It's not marketed as the 360 S because it's the only version that's actually manufactured and sold now.
An identifier for the manufacturer's sake would be akin to the CECH codes that Sony use for the PS3, which provide a lot more detail about each specific model than "Xbox 360 S" does.
Incidentally, this qualifies as the most boring argument of my life.