TORONTO >> As the cast and makers of “Stronger” collectively rose to take a bow after the film’s Toronto International Film Festival premiere, Jake Gyllenhaal realized that Jeff Bauman, whom he plays in the film and who wears prosthetic legs, was still sitting, overwhelmed with emotion.

“Jake was like, ‘Get up!’” Bauman said. “And I stood up.”

“As soon as he got up, everyone else stood up,” Gyllenhaal said. “I realized: This movie just showed them everything he went through just for that moment. I’ve never had an experience like that making a movie.”

“Stronger,” directed by David Gordon Green, is the kind of movie that holds as much drama off the screen as on it. The movie chronicles Bauman’s struggles after a bomb explosion tore through his legs while he was waiting by the finish line of the 2013 Boston Marathon. He was there to greet his on-again, off-again girlfriend, Erin Hurley, who had previously chided him for never “showing up.”

“Stronger,” based on Bauman’s 2014 memoir, is an undoubtedly inspiring story, but maybe not in the way you’d expect. Honest, painful and funny, it avoids the familiar Hollywood beats for a more truthful tale of personal growth. “The big moments of our lives don’t happen in a close-up,” says Gyllenhaal.

“Stronger” captures Bauman, now 31, recalibrating his life after the tragedy, still struggling with relationship and drinking problems that predated the bombing and chafing at the role cast upon him as a heroic symbol of “Boston Strong.” Bauman instead saw himself merely, he says, as: “Just a dude with no legs.”

Bauman’s modesty remains, but he’s also come to terms with being someone who gives hope to others, who can now connect with a wide world of amputees, war veterans and other sufferers trying to get by. One memorable scene, taken from a real experience, shows Bauman mobbed at Fenway Park and listening to story after story.

“There’s so much love coming at Jeff,” says Gyllenhaal. “People line up — they really do — to talk to him. They’re like: ‘This thing happened to me,’ ‘That thing happened to me.’ We are not alone in all that, and that’s what his story says.”

Meeting for an interview at a Toronto hotel shortly after the film’s festival premiere, the close bond between Gyllenhaal and Bauman was plainly evident. In the two and a half years since they began working on the movie together, they’ve gotten to know each other well through Gyllenhaal’s regular trips up to Boston to spend time with Bauman and study how he moves. Bauman came to New York to see Gyllenhaal on Broadway. They threw out the first pitch at Fenway together.

“Since we first met, I think he’s a totally different person now,” Gyllenhaal says. “Particularly in the past year, since getting sober. I think he’s been much more open. When we first met, trying to learn about him and figure out what was going on was a little harder. And now I feel like I know him better than even when I played the role.”

“Bromance” is a term that has often been applied to their relationship, but Gyllenhaal, 36, is more like an encouraging older brother. He’s helped Bauman through hard times (he and Hurley, previously married and with a three-year-old daughter, Nora, have separated) and gamely accepts Bauman’s playful chiding — like his questioning the depth of the New York-based Gyllenhaal’s Red Sox fandom.

Jake: “I am a Sox fan. I just wear a Yankees hat, but I am a Sox fan.”

Jeff: “He doesn’t wear a Yankees hat around me.”

Jake: “That’s true.”

Jeff (derisively): “He’s a Warriors fan.”

Jake: “Easy.”

They’ve been inseparable while strolling down red carpets and promoting “Stronger.” Last week, they showed the film to patients and staff at the Spaulding Rehabilitation Hospital, where Bauman worked on his recovery and where they filmed scenes for the movie.

But in the time they’ve been making “Stronger” (Gyllenhaal is also a producer), both say Bauman has dramatically grown. He’s now 15 months sober and studying engineering in college. Working at Costco at the time of the bombing, Bauman now hopes to work for a prosthetics company. He also moved out of his mother’s apartment and into his own place. Gyllenhaal considers it the film’s biggest accomplishment.

“I took my hand off the pause button,” says Bauman. “I had my life on pause. You get stuck, especially when you’re drinking and isolating. I started homing in on what I wanted to do as a person. Just try to grow up.”

When Gyllenhaal first met Bauman, he was struggling to adjust to the prosthetic legs. Now, he confidently goes up and down stairs, unaided. Bauman, still reluctant to take any credit, praises the technology. But Gyllenhaal prods him, still trying to get Bauman to take some credit.

“I wish you could stand where I stand when you walk through,” Gyllenhaal says, “and people just go, ‘F—-ing awesome.’”