Warning! Spoilers ahead for Lightyear
While Lightyear is an action-packed look into the origins of Toy Story's iconic Space Ranger, Disney and Pixar essentially repeat Buzz Lightyear's character arc from his first origin movie. As seen in the animated feature that kicked off Disney's Buzz Lightyear of Star Command cartoon series, Buzz wanting to be a solo hero was a major part of that film released in 2000. Likewise, the framing devices for both the cartoon and Pixar's new Lightyear movie starring Chris Evans are also the same.
Released as a direct-to-video film from both Disney and Pixar to launch the Buzz Lightyear of Star Command animated series, Buzz Lightyear of Star Command: The Aventure Begins had Tim Allen returning to voice the main character he'd portrayed in the first two Toy Story movies. Already enlisted as a Space Ranger defending the Galactic Alliance as part of the Universe Protection Unit, Buzz Lightyear is one of Star Command's best. However, he loses his partner, Warp Darkmatter, who's seemingly killed in action. This results in Buzz's determination to work alone, uninterested in new teammates, or in receiving help of any kind. However, a nefarious plot from the Evil Emperor Zurg eventually convinces Buzz that he can't save the galaxy alone, resulting in him forming a new team with the three rookies the feature film introduces: the robot XR, Booster Munchapper, and Princess Mira Nova. As such, Team Lightyear's adventures were depicted in the subsequent cartoon series that followed, with Buzz now being voiced by Patrick Warburton in the actual series.
By comparison, Buzz's character arc in Lightyear is very similar to Buzz Lightyear of Star Command: The Adventure Begins, repeating many of the same narrative beats. Determined to take on every challenge and threat by himself, Buzz is extremely resistant to taking on teammates who are also rookies (Izzy, Mo, Darby, and Lightyear's robot cat, Sox). However, the threat of Zurg eventually convinces Buzz that he can't save the day alone, resulting in him forming a new team of Space Rangers by the end. While Buzz doesn't lose a partner as he does in Star Command, the character arcs are extremely similar — including their resolutions.
It should also be noted that the framing devices for both Buzz Lightyear spinoffs and their relation to the Toy Story franchise are mirrored as well. Lightyear begins with a message saying it was the movie that Andy watched featuring one of his favorite toys: Buzz. While working with the same concept, Buzz Lightyear of Star Command: The Adventure Begins's framing device is arguably better as it features a CGI opener produced by Pixar with Andy's toys all sitting down to watch the cartoon that inspired their friend Buzz.
Lightyear director Angus MacLane has commented that Pixar didn't really consider having canonical connections to Buzz's TV show, but it's evident that many story beats were taken from Buzz's original origin story. As such, Buzz Lightyear essentially has a second chance 22 years later for fans to experience his origins as a Space Ranger with Disney and Pixar's Lightyear. That being said, Buzz Lightyear of Star Command and its Adventure Begins film will likely still hold a place in many fans' hearts all the same.