The concept of a test that is the same every time is rather limiting...
If it really involves a Kobayashi Maru every time, we should see a look of recognition on Saavik's face (and hear the "...Damn." gasp) when the name gets mentioned the first time in the simulation. Saavik shouldn't be ignorant of the existence of the famed "Kobayashi Maru test". That is, if it existed: TWoK keeps it vague, only referring to the repeated use of a "no-win scenario", which involves "rescuing the ship", and allows for the scenario to be drastically different from cadet to cadet (or lieutenant to lieutenant for that matter). Although of course Kirk might have chosen to throw at Saavik the exact same scenario he himself once faced, just to celebrate the anniversary or whatnot.
McCoy in the 2009 movie in turn leaves nothing unclear about it always being about the Kobayashi Maru. Although of course it might be that there are multiple final exams to the command course, and the only one of interest is the one Kirk is planning on retaking - the one with the reputation of being unwinnable.
Spock in both universes might well be the guy who designed the especially sadistic Kobayashi Maru scenario, as opposed to all those other no-win scenarios that don't feature his trademark vessel-in-distress. For all we know, Spock in both universes did take such a test, only not the exact one he would later design that would be associated with the ship name.
Timo Saloniemi