(covers information from several alternate timelines)
A Class III neutronic fuel carrier or 3rd class neutronic fuel carrier was the designation used to classify a type of 23rd century fuel carrier capable of hauling several metric tons of neutronic fuel as well as several hundred passengers.
In the Kobayashi Maru scenario, the Kobayashi Maru was a 3rd class neutronic fuel carrier. (Star Trek II: The Wrath of Khan; PRO: "Kobayashi") Likewise, in the alternate reality, the USS Kobayashi Maru was also a ship of this class. (Star Trek)
The sidebar data was extracted from the display graphic appearing in the scenario describing the Kobayashi Maru, which appeared in both The Wrath of Khan and "Kobayashi".
In dialogue, it was referred to as a "3rd class" carrier, whereas on the display it was referred to as a "Class III" carrier.
John Eaves and Alex Jaeger designed the Kobayashi Maru for Star Trek. They based the design on Roger Sorensen's blueprints from 1983 of the prime universe Class III neutronic fuel carrier Kobayashi Maru . Although the Eaves blog also cites the cover of the novel The Kobayashi Maru,  which shows a depiction of a Tritium-class starship (β), originally designed by Rick Sternbach for the Spaceflight Chronology. (p. 130), the sketches and finished design bear little or no resemblance to that ship.
In the opinion of Industrial Light & Magic art director Alex Jaeger, the starship Kobayashi Maru had a similar design to the USS Excelsior (β) that was planned to feature in the film Star Trek but did not make the transition to the screen (although it was essentially a dark-colored variant of the Armstrong-type). Jaeger specifically commented about the Kobayashi Maru, "It resembled the Excelsior, but was more of a cargo version." (Cinefex, No. 118, p. 60; Star Trek - The Art of the Film, p. 59)