To describe just how meaningful the Lindsay Lohan-Jamie Lee Curtis remake of “Freaky Friday” was to a 13-year-old in 2003, I’ll use an anecdote. Shortly after seeing the movie with my mom, she asked me if I wanted to get a second piercing in my ear, a gesture that meant the world to an awkward tween desperate for some edge. My mom understood that Lohan in that movie was the pinnacle of cool, and that she could in turn gain some cred, just like Curtis on screen, if she submitted to my whims. Meanwhile, I got a little closer to approximating Lohan’s perfect teen aura. In the early 2000s she was an influencer before that was even a term, the most famous girl in the world, who seemed destined for unstoppable greatness.

That was the magic of the movie, directed by Mark Waters, which updated the body-swap plot to the early ’00s with a lot of heart and a little bit of pop punk. The movie succeeded because of how equally balanced it was to the perspectives of mother and daughter-with Curtis and Lohan both turning in genius comedic performances that were funny but never felt mocking.

Still, as much as I loved “Freaky Friday,” it was hard to imagine that a sequel coming more than 20 years later could recapture any of the glory of its predecessor. After all, in the interim years we watched Lohan’s very public fall from glory, hounded by tabloids as a victim of that era’s cultural misogyny. For a while she seemed to exist not as an actress but as a curio — remember “Lindsay Lohan’s Beach Club,” anyone? — only to tiptoe her way back to respectability by way of corny Netflix Christmas movies.

And yet “Freakier Friday,” directed by Nisha Ganatra, has defied the odds. It’s charming and genuinely sweet, and it made me both giggle and tear up. That alone is a win.

Of course, in many ways Curtis never left us. During a light interregnum from major film work, she remained in the public eye with her warmly incessant Activia TV commercials. Then she made a blazing return to her old Halloween stomping grounds and won an Oscar for “Everything Everywhere All at Once.” And her funny, outspoken social media presence — plus an “I’ll do anything” approach to roles — has made her easy to root for.

Blessedly, Lohan seems back in her old groove again playing Anna Coleman, the once rebellious teenager who’s now a single mom. She’s relatively hip but still, you know, a mom. We learn Anna’s band Pink Slip did achieve some level of fame, but Anna herself left the rock ’n’ roll lifestyle to become a manager for pop stars. Her daughter Harper (Julia Butters) is now the rebellious one, but her form of acting out is different from what her mom’s was. Harper is a surfer girl with a “no triggering” sign on her door who sneaks out of her room early to catch some waves.

Curtis’ Tess, meanwhile, has become an overly involved grandmother who podcasts on the side. The Colemans’ rhythms are put to the test when Anna falls hard for Eric (the dreamy Manny Jacinto), a British chef. He just happens to be the widower father of Harper’s high school enemy Lily (Sophia Hammons), whose fashion-obsessed snobbery doesn’t jibe with Harper’s laid-back vibes.

About a year later, Anna and Eric are about to get married, and the girls still hate each other. That resentment grows even stronger when Harper learns Anna is planning on moving them all to London. It’s a development that also irks Tess, who doesn’t want their whole family abandoning her.

So they all have a lot of stuff to work out when the body swapping happens, which it does thanks to a psychic/reiki healer/general entrepreneur who’s hired as the entertainment at Anna’s bachelorette party, played to hilariously dotty perfection by Vanessa Bayer. Anna gets Harper’s body and vice versa, while Tess gets Lily’s and so forth. The latter swap gives Curtis the chance to exercise British slang to great effect. In fact, playing a younger person in her own skin is maybe the perfect use of Curtis’ on-screen intensity.

The adults in teen bodies relish their youthful metabolisms and their ability to stand up without their joints hurting. The teens in adult bodies scheme to break up their parents by reaching out to Anna’s ex Jake (Chad Michael Murray, with unexpectedly one of the funniest bits in the whole movie). Eventually, thanks to myriad misunderstandings, they all learn something about one another’s perspective along the way.

Occasionally, the gags are a bit cringey. Harper and Lily (now looking like Anna and Tess) befriend Anna’s emotionally vulnerable client (Maitreyi Ramakrishnan) and try on hideously poofy dresses from a fashion shoot. I have a hard time believing Gen Z would think these fashions are actually cool. But the goofiness is part of the fun, and it’s offset by deeply felt performances from the cast, particularly Lohan and Butters.

Butters, who wowed audiences as the tiny girl who gives Leonardo DiCaprio the what’s what in “Once Upon a Time in Hollywood…,” is extraordinary in conveying the adult longings of a grown-up trapped in her daughter’s skin. As Harper-pretending-to-be-Anna, you see Lohan heartbreakingly realize just how loved her mother is by the man she wants to get rid of because of her own selfish desires. It’s an absolute pleasure to watch the actress once again turn in a performance that’s alternately as nuanced and silly as this one.

Ultimately, what makes “Freakier Friday” successful is that it understands what made the first one so good wasn’t just the goofy high jinks and catchy soundtrack. (Though speaking of that soundtrack: “Take Me Away” and “Ultimate,” both tracks from the original, are back and remain bangers.) Those are fun, but it was the mother-daughter connection that elevated it to modern classic. Freakier Friday adds two more generations to the mix and comes out with a touching story about how we all have to make little sacrifices for the happiness of the ones we love.