For a movement dedicated to shocking the masses and jabbing a safety pin into social pretensions, punk also had a moral streak. It saw itself as a pure corrective to bloated, baroque rock music and posh, remote rock stars. In “Pistol,” Danny Boyle’s rock-bio of the Sex Pistols, John Lydon (Anson Boon), a.k.a. Johnny Rotten, claims that his group is “the most honest band to have ever existed.”

Fact check: It’s complicated. The Pistols were certainly blunt — to the public, to their fans, to each other. But they were also, as “Pistol” tells it, an invention, a carefully assembled artifice from the impresario Malcolm McLaren (Thomas Brodie-Sangster, “The Queen’s Gambit”), the impish rock ’n’ Rumpelstiltskin who exacted a high price for spinning them into gold.

Was the band a needed blast of power-chord candor, or, to borrow the title of the eventual Julien Temple mockumentary about them, a great rock ’n’ roll swindle? In pop culture, both things can be true. Two very different new shows — “Pistol,” about British rebellion, and “Angelyne,” about California-style self-invention — suggest that an artificial creation can be more real than reality.

“Pistol,” as a series, is something of a contradiction. Directed by Boyle and written by Craig Pearce, it celebrates the punk spirit of authenticity and exudes love for the Pistols’ yowling chaos. But this story of yobs spitting gobs turns into a busy production that’s as bombastic and overly filigreed as a prog-rock keyboard solo.

The six-part “Pistol” is based on the memoir “Lonely Boy: Tales from a Sex Pistol” by the band’s guitarist, Steve Jones. (The series — deep breath — is an FX production that will not air on FX but will drop all six episodes on Hulu on Tuesday, because this is what TV is in 2022.) This makes Jones (Toby Wallace) the point-of-view character, whether he’s suited for the job or not.

A baby-faced, miscreant bundle of hormones who escaped an abusive home, Jones catches a break by meeting McLaren, a sometime music manager who runs the transgressive boutique SEX with the designer Vivienne Westwood (Talulah Riley). McLaren recasts Jones from singer to guitarist in his band, the Swankers, which is renamed the Sex Pistols, and finds his frontman in the clever, sneering Lydon.

Jones does not know how to play guitar. Lydon is not sure that he can sing. But this is no matter to McLaren, a capitalist Robespierre given to pronouncements like “I don’t want musicians, I want saboteurs!”

McLaren’s real talent is casting, and “Pistol” aces this part of the audition, too. Boon captures Lydon’s spiky abrasiveness (and hair) and lends him a disarming thoughtfulness. The concert scenes, which reproduce much of the Pistols’ brief catalog, explode with delirious violence.

But while “Pistol” amply looks and sounds the part, it struggles with the lyrics. It aims to place the band within the larger context of an economically and culturally stagnant 1970s Britain, but at heart it’s a standard behind-the-music tragedy. It becomes more so once the band recruits Lydon’s mate Sid Vicious (Louis Partridge), who’s more adept with a broken bottle than with the bass, and who leads “Pistol” to revisit the material of the film “Sid and Nancy.”

Boyle’s intrusive direction suggests a higher ambition, but it gets in his way. The series triple-underlines key moments; when Sid’s “vicious” hamster bites him, giving him his nickname, you expect a bell to ring. “Pistol” is especially fond of explanatory documentary footage. When Lydon leaves the band and Sid Vicious, replacing him on vocals, agrees to record “My Way,” we get a clip of Frank Sinatra, lest you miss the reference.

The most interesting material in “Pistol” is just outside the band’s orbit, especially its attention to how punk fashion intersected with — and even predated — the music. (Besides Westwood, the punk fashion icon Jordan — Maisie Williams, straying far from Winterfell in a shock of dyed hair — presides over the series like a messenger from the future.) But this theme gets upstaged by the rock-star story, just as it was in life.

“Pistol” is conscious of the advantage that its rocker dudes had in claiming the revolutionary credit denied to women rebels. Westwood tells McLaren that he does little more than co-opt her ideas about creative destruction, but adds, “I’m used to it.”

But the series tends to shortchange its women itself. “Pistol” makes clear that Jones’s friend and sometimes lover Chrissie Hynde (Sydney Chandler), who will eventually front the Pretenders, is the more gifted and disciplined musician. But just as she’s frustrated in breaking into the boys’ club, her character in “Pistol” often falls into a sitcom-like sensible-best-female-friend role.

The series repeatedly flicks at intriguing peripheral characters, as in Episode 3’s portrait of “Pauline” (Bianca Stephens), the mentally ill woman who inspired Lydon’s lyric for “Bodies.” Much as the Sex Pistols became a repository for the whims and notions of McLaren, “Pistol” becomes a vehicle for tossing in more interesting stories, which occasionally fall out of the back of the tour van as it careers down a familiar road.

At first blush, Peacock’s “Angelyne” has little in common with “Pistol.” It explores the mystery and the will to celebrity of its title character (Emmy Rossum, “Shameless”), who made herself into an icon by posing hood-ornamentlike on the billboards of Los Angeles in the 1980s.

But this sex goddess, much like the Sex Pistols, is also a work of pop-culture artifice, whose self-creation has roots in the Los Angeles punk scene. She’s her own Malcolm McLaren, and she sits as comfortably in her mythmaking as in the driver’s seat of her pink Corvette. First as a singer in her boyfriend’s woeful band, then as a professional celebrity, she lives by the credo: “I don’t want to be famous for what I do. I want to be famous for who I am.”

But being who she is takes a lot of doing. Rossum, who shepherded the project over years, gets a spectacular acting showcase (complete with the kind of body-armor prosthetic transformation that is de rigueur in current docudramas). Nancy Oliver and Allison Miller, the creator and showrunner, give the series an astute feminist grounding under its hard candy shell.

Angelyne’s performance, after all, is a critique of objectification. She made herself an exaggeration of what pop culture wanted from women, as manifested in decades of starlets and sex kittens. Her allure, “Angelyne” understands, came not just from her engineered curves but from withholding her secrets in a culture that sees bombshells like her as ripe for plunder.

Her origins finally emerged in a 2017 Hollywood Reporter exposé, whose raw material the series relays through obtrusive mock interviews with characters, many of them renamed, lightly fictionalized versions of real people. We hear from Jeff Glaser (Alex Karpovsky), the reporter sleuthing Angelyne’s story; Harold Wallach (Martin Freeman), the businessman she charms into backing her billboard campaign; her aide and fan-club president (Hamish Linklater); and Angelyne herself, enthroned on a love seat shaped like two rose-colored lips, who interjects to dispute others’ versions of events.

Through this docu-“Rashomon” device, “Angelyne,” like Angelyne herself, works to control the viewer’s perception of it. You might conclude, for instance, that Angelyne was an influencer before Instagram, a Kardashian before reality TV, a savvy interpreter of the ways women access power. But you don’t need to — “Angelyne” does it for you, repeatedly.

The series is strongest, even transcendent, when it gives the talking heads a break and takes imaginative flight. The final episode, which delves deep into Angelyne’s biography, is almost theaterlike in the way it has characters step outside themselves and comment on their situations. It dramatizes the moving back story laid out in the Hollywood Reporter investigation, then shifts focus to Angelyne’s fantasy of herself as a space-faring alien, come to liberate Earthlings from terrestrial boredom.

Maybe Angelyne is an idol made of plastic. But what’s so great about authenticity? What’s so important about nailing down the facts of one meta-celebrity’s origins, compared with the concoction of glamour she offered a city of motorists stuck at traffic lights? Perhaps, “Angelyne” suggests amid a TV landscape glutted with “true story” dramas, a story can be true even if it isn’t real.

Back on planet Earth, the real-life Angelyne has criticized the series (the same reaction you’d expect from Rossum’s version of her). But to this viewer, at least, it’s a sincere tribute to the parthenogenesis of a pinup. Angelyne, it argues, became her own work of Pop Art — even if, to paraphrase the Sex Pistols’ “E.M.I.,” she only did it ‘cos of fame.