In the 2015 film 'The Martian', the mission that leaves Mark Watney behind is Ares III.
Ares III is NASA's third crewed mission to Mars, commanded by Melissa Lewis. The crew lands in Acidalia Planitia for a planned 31-sol expedition, but a severe dust storm threatens to topple the Mars Ascent Vehicle. During the emergency evacuation, flying debris strikes Watney, and his crewmates mistakenly believe he has died.
The remaining astronauts launch from Mars aboard the MAV and return to the Hermes, leaving Watney alone in the surface habitat. When he regains consciousness, he must ration supplies, repair equipment, establish communication with Earth, and grow potatoes using limited resources. His training as a botanist and mechanical engineer becomes essential to his survival.
Ares IV is the next Mars mission mentioned in the story and becomes part of the rescue planning, which makes it an easy mix-up. Apollo 13 is a real 1970 lunar mission, not a mission in the film, while Ares I and Ares V are different fictional missions in the broader program.