He had silky black ears and a dapper bow tie. He was the Vice-Presidential pet, property of the Pence family; he was an Instagram star, rubbing shoulders with Whoopi Goldberg. He accompanied his “Grampa” to the Oval Office and the Capitol; he married a boy bunny.

By now, you have probably heard the tale of two bunny books. Bunny Book 1, “A Day in the Life of the Vice President,” was written by Pence’s daughter Charlotte, twenty-four, and illustrated in demure, muted watercolor by the Second Lady, Karen Pence. It follows Marlon Bundo, the real-life “Bunny of the United States of America,” or BOTUS, as he shadows Vice-President Pence over the course of a typical day in Washington. (The forty-page volume, rated at a second-grade reading level, sits at No. 4 on the Amazon best-seller list as of this writing. A portion of the sale proceeds are flowing to A21, an anti-human-trafficking organization, and to the Riley Hospital for Children, in Indianapolis.)

Bunny Book 2 was dreamed up by John Oliver, of HBO’s “Last Week Tonight.” It was written by the comedy writer Jill Twiss; the whimsical illustrations are by E. G. Keller. Titled “A Day in the Life of Marlon Bundo,” the tale is both a satire of the Pence product and a sweet standalone story about love, acceptance, and civic responsibility. In this version, BOTUS is whisked off his feet by a handsome brown fellow named Wesley—his aquamarine spectacles match Marlon Bundo’s checkered bow tie—and the two overcome the strenuous objections of a mean stinkbug (who looks like Mike Pence) in order to get married. (All proceeds from the book, Oliver has announced, will go to the Trevor Project and AIDS United.)

While Charlotte Pence, whose father is infamous for his opposition to L.G.B.T. rights, greeted the news of an unauthorized companion work with good humor (“We have two books that are giving to charities that are about bunnies, so I’m all for it really,” she told Fox Business), her publisher, Regnery, lamented that “anyone would feel the need to ridicule an educational children’s book and turn it into something controversial and partisan.” Grumbling aside, Oliver’s parody has topped the Amazon best-seller list, beating not only Pence’s book but also the memoir of the former F.B.I. director James Comey. A new printing has been ordered to replace the hundred and eighty thousand copies that ran out within forty-eight hours.

The less said about the Pence book, the better, alas. It attempts a loose anapestic trimeter that is mostly embarrassing:

Some people call me BOTUS—

A name any bunny would love.

It means “Bunny of the United States”—

A job I am very proud of!

This Marlon Bundy finds Grampa extremely impressive. He notices that people are frequently “lining the streets” and “waving their flags” at Grampa’s motorcade, and Grampa “always gives them a thumbs-up.” The Vice-President works hard presiding over the Senate, advising the President, and talking to “people from across America” who “come to share stories and questions and problems.” (Grampa “helps answer each one,” Marlon Bundo marvels.) The word “important” appears three times in four pages. As night falls, Grampa and Marlon pray together, and the bunny thinks over the events of the day: “I remember how blessed I am / To call this great nation my home.”

I feel sheepish knocking a kids’ story about the least complicit member of the Second Family, but the self-satisfaction and mediocrity on display here are galling. Meanwhile, the Oliver parody is sincerely delightful—full of the attentive details and poetic grace notes that distinguish good children’s books. (The Vice-Presidential residence is an “old, stuffy house”; two insect friends bend over a miniature checkerboard; the stinkbug’s podium is emblazoned, wonderfully, with a stinkbug logo.) That the joke version of the product feels realer and truer than the product itself somehow suits our post-fact world, salted with “fake news” and cable-news chyrons that prove stranger than fiction. “Marlon Bundo” pays homage to classic children’s titles (a spray of purple lupines across the cover conjures “Miss Rumphius”) and replaces Pence’s stilted rhymes with a freer set of rhythms and repetitions—some of which also gesture poignantly at our leading man’s pre-Wesley sadness. “I woke up all alone. Then I ate a fine bunny breakfast all alone, while I watched the news . . . all alone,” Bundo says.

Oliver’s book delivers some subtextual treats for adults. Here is the not-quite-safe-for-work account of Marlon Bundo and Wesley getting to know each other: “Once we had hopped through every part of the garden, we didn’t want to stop hopping. So, we hopped right inside the old, stuffy house. We hopped up and down the creaky stairs and made beautiful, creaky stair-music together.” Never in the annals of euphemism have bedsprings squeaked so delicately. The dashing Wesley first appears in a halo of golden light that seems precision-engineered to annoy evangelical grampas. (“That was when I saw Him,” Marlon Bundo swoons, capitalizing the H. “He was bunny-beautiful.”) Twiss approaches the gay-acceptance elements with gentle, moving didacticism. When Bundo announces that he and Wesley are engaged, all his friends shout “Hooray! . . . Because that is what friends say.” If the implicit theme of “A Day in the Life of the Vice President” is Pence’s power and importance, his goodness and piety, the explicit message of Oliver’s book is, in the words of Scooter the turtle, “Everyone is different. And different is not bad.” (“I am different too,” offers Mr. Paws, a dog, on the funniest page of the volume. “Sometimes I sniff butts and I don’t know why.”)

BOTUS and Wesley manage to wed after they and their friends band together and vote the stinkbug off his podium. (Subtle.) In that sense, the second bunny book foregrounds the beauty of American democracy, its capacity to realize people’s hopes and aspirations, more effectively than the first, with its tepid talk of “this great nation.” Oliver’s title possesses the added benefit of dramatic stakes: Will the marriage occur? Will Marlon Bundo ever assuage his loneliness? There is, come to think of it, no metric by which the parody bunny book does not outshine the original, unless you want to fault Twiss and Oliver for not explaining what E.E.O.B. stands for. (The Eisenhower Executive Office Building; thank you, Charlotte Pence.)

Bunnies, of course, are sites of whirling semiotic complexity. They are children’s-book staples, with starring roles in “The Runaway Bunny,” “The Velveteen Rabbit,” and “Goodnight Moon,” not to mention the myth of the Easter Bunny and the tales of Beatrix Potter. Linked to infancy, these creatures have enormous eyes, twitchy noses, floppy ears, thumping feet. They look soft and cuddly and innocent and defenseless, a suite of attributes warped to sardonic effect by the movie “Donnie Darko.” As pets, bunnies evince zero edge and exude a whiff of basicness. At the same time, they have served as sex symbols since long before the phrase “bunny girls” first hopped into Playboy, in 1960. The cliché “fuck like a bunny” goes back at least to 1978; “fuck like rabbits” dates to 1897. As the language blogger John Kelly recounts, the rabbit synonym “coney” inspired associations with “cunny,” a slang term for the vagina, as early as the fifteen-hundreds. (Mike Pence might be fascinated to learn of the linguistic ties between “cunt” and “country.”) In the wake of “Sex and the City,” a rabbit may also summon thoughts of the character Charlotte’s temporary vibrator addiction. BOTUS takes his place in the tradition of lusty, naïve leporidae. Only a bunny could be at once so pure and so dirty—so perfectly suited to square the Pences’ blandness with the subversions of “Last Week Tonight.”