Someone cued the music, and the cast broke into an energetic dance number. There came Cha-Cha DiGregorio (Yvette Gonzalez-Nacer), rubbing her skirt suggestively on her thighs, just like in the 1978 movie, as a Rydell student dragged his date across the floor by one leg, just like in the 1978 movie.

Still, Mr. Kail and his choreographer, Zach Woodlee (“Glee”), are most definitely not just putting forward a carbon copy of what “Grease” fans have seen before. Their goal is to combine elements from the movie and the stage version that preceded it while adding two new songs (written by Tom Kitt and Brian Yorkey, known for Broadway’s “Next to Normal”) and updating others.

“We have affection for the movie and the stage play just as much as everybody else,” Mr. Kail said. “But it’s not about trying to redo those. It’s trying to capture the spirit.”

Mr. Kail pointed to casting as an area that overtly bears his stamp. Instead of sticking to the blueprint of Frenchy created by Didi Conn in the movie — cartoon voice, wide eyes — he veered toward introspective and arty, hiring the Canadian singer-songwriter Carly Rae Jepsen to play the Beauty School Dropout. (Ms. Conn will pop up as Vi, the world-weary Frosty Palace waitress.) Diversity was important; Keke Palmer plays Marty, Carlos PenaVega was entrusted with Kenickie, and Boyz II Men will perform in the Teen Angel role that Frankie Avalon made famous.

Ms. Hudgens, who starred as “Gigi” on Broadway last season but is still best known as the super-sweet Gabriella from the “High School Musical” series, was cast as the caustic Rizzo. “When my agent called I was, like, ‘Huh?’” Ms. Hudgens said, making a face. “I never really thought of myself as Rizzo. But then I thought about it, and I realized it would be a really cool challenge.”

How has Ms. Hudgens made the character her own? “Body language is big,” she said. “It wasn’t all that hard in the end.”