Decidedly anti-sensationalistic, Alison Leiby’s shrewd and funny personal monologue plays downtown. Uptown, a staged reading focuses on a gruesome case.A few nights after the leak of the Supreme Court draft opinion that would overturn the right to abortion protected by Roe v. Wade, the comedian Alison Leiby walked onto the stage of the Cherry Lane Theater, in Manhattan’s West Village, to greet the audience before her monologue.“How are we doing?” she asked, taking the temperature of a friendly crowd that had more men in it than you might expect. Then, easily: “The show is exactly the same as it was before we lost all of our rights.”Low-key sardonic, politically charged humor it would be, apparently. We might have guessed as much from the title of the insightfully funny piece she was about to perform: “Oh God, a Show About Abortion.”It is probably true, in terms of Leiby’s script and Lila Neugebauer’s direction, that the monologue — constructed around an account of the abortion that Leiby had three years ago, at 35 — has not changed. But the atmosphere surrounding abortion rights has; it’s more charged, more urgent, more anxious. And the audience always brings the outside world into the room.So here is the first thing you need to know about Leiby’s abortion story: In a smart and entertaining show, full of observations about the sometimes painful messiness of female bodies — menstruation, childbirth, lactation — and the social pressure to put on a happy face about all of it, her trip to Planned Parenthood is the least dramatic, most calmly straightforward part.“Does this feel anticlimactic to you?” she asks, when she’s done retelling it.She knows it must, because back when it happened, she’d expected something more lurid, too.“I think that I thought I’d have some kind of Scarlet A that tells everyone I had an abortion,” she says, “which would have been devastating because it’s private, and also red clashes with my complexion.”A laugh line, sure, but that bit about the fear of the Scarlet A? It lands.“Oh Gosnell: A Show About the Truth” is a staged reading based on court records that features the cast members, from left, Roxanne Bonifield, Kaché Attyana, Benjamin Standford and Andrea Edgerson.Russ RowlandA couple of miles uptown, at the Chain Studio Theater on West 36th Street, is a show that announced its New York run as “Oh Gosnell: The Truth About Abortion” — a tabloid title with stalkerish overtones, especially given that its own news release mentions Leiby’s show.A publicist for “Oh Gosnell” said that the creation of the play was inspired by Leiby’s comic monologue. “They laugh about it — we tell the truth about it,” says the website of the play now going by the name “Oh Gosnell: A Show About the Truth.”It’s written by Phelim McAleer, who is credited on IMDB as being a producer of the yet-to-be-released film “My Son Hunter,” starring Laurence Fox as Hunter Biden, and as a writer and a producer of “Obamagate,” starring Dean Cain, which The New York Post described as a play that had its premiere on YouTube. His other plays include “Ferguson,” about the 2014 police shooting of Michael Brown.Laughter and truth are not mutually exclusive, of course, even if McAleer, a right-wing provocateur whose program bio calls him “a veteran investigative journalist,” implies otherwise.As for conveying any general truth about abortion, rather than specific truths about the gruesome case of Kermit Gosnell — a Philadelphia physician convicted in 2013 of first-degree murder for killing three babies after botched late-term abortions — it doesn’t. Neither is it constructed to persuade.The script for the play, simply titled “Gosnell,” says that it was “compiled, verbatim, from grand jury and criminal trial transcripts” in the Gosnell case. In a spare, somewhat murky staged reading directed by David Atkinson, it has a cast of seven that includes a compelling young actor named Kaché Attyana, who I hope will soon get better work.“The first thing I want you to be assured of, ladies and gentlemen,” a prosecutor (Roxanne Bonifield) says, close to the top of the show, “is that this is not a case about abortion.”For emphasis, she repeats that assertion. Maybe McAleer, the co-author of a book about the Gosnell case, and a producer and co-screenwriter of the 2018 movie “Gosnell: The Trial of America’s Biggest Serial Killer,” didn’t hear her?Then again, in a program note, McAleer writes of the Gosnell trial: “Perhaps the desire to suppress information was why no national media covered the story. There is a reluctance to shine a spotlight on abortion in the U.S. Few people are prepared to go behind the doors and tell the truth of what is really happening there.”Heidi Schreck in her play “What the Constitution Means to Me,” which opened on Broadway in 2019.Sara Krulwich/The New York TimesThe problem with saying that no national media covered the story — well, his own show contradicts that right off the bat, when images of news clippings about the case include one from The New York Times. (Projections are by Meghan Chou.)As for going behind those doors, women do that every day, seeking abortion care. Leiby did it. I’ve done it. My mom did it, too, pre-Roe v. Wade, to save her life from an ectopic pregnancy before my brothers and I were born.Telling the truth about abortion, though — speaking of those experiences, that is, in a culture where abortion remains heavily stigmatized — well, that is rare.Which is maybe why Leiby expected to feel something more sensational than relief after her own abortion.“I thought I’d spend the next few days or months staring out the window like I’m in a depression medication commercial,” she says. “I thought I would carry sadness and emptiness with me everywhere I went.”Kidding, a little bit? Probably. But the notion of abortion as an automatic trauma is pretty deeply rooted in the culture, and it’s not often interrogated onstage. Which leaves the mystery intact.And, conversely, gives the shows that do discuss it an added potency — like Ruby Rae Spiegel’s “Dry Land,” which harnesses the ticking-time-bomb feeling of an unwanted pregnancy, and Lightning Rod Special’s “The Appointment,” which juxtaposes wild musical satire with the crisp quiet of an abortion clinic. And, of course, Heidi Schreck’s “What the Constitution Means to Me,” which put an abortion story on Broadway.In the Signature Theater revival of Suzan-Lori Parks’s play, Christine Lahti (right, with Joaquina Kalukango) portrayed an abortion provider. Richard Termine for The New York TimesWhen Leiby mentioned the Scarlet A, I thought of Suzan-Lori Parks’s take on “The Scarlet Letter” — the one of her Red Letter Plays whose title we can’t print here — with its heroine, Hester Smith, who is described in the list of characters as “the Abortionist.” Kia Corthron’s “Come Down Burning,” which also has a heroine who performs abortions, makes a clear connection between the option to safely end a pregnancy and women’s ability to control their own lives.Then there is Ciara Ni Chuirc’s “Made by God,” which had its premiere this winter at Irish Repertory Theater: a drama about a shame-filled Irish teenager who died alone with her newborn in the 1980s, and about the seismic shift in public opinion that led Ireland to legalize abortion in 2019. The play’s principal anti-abortion character is an American interloper.Leiby — who reports, incredulously, that she whispered the phrase “an abortion” to Planned Parenthood when she called to make an appointment for one — means her monologue to start people talking about theirs.Beyond that, though, her show makes a broader point: about the need for women to be able to decide what they want and don’t want, and shape their existences accordingly.“I’m a woman who did something she needed to do,” she says, “to protect the life she built for herself.”It’s not funny, but it’s true.Oh God, a Show About AbortionThrough June 4 at the Cherry Lane Theater, Manhattan; cherrylanetheatre.org. Running time: 1 hour 10 minutes.Oh Gosnell: A Show About the TruthThrough May 15 at the Chain Studio Theater, Manhattan; ohgosnell.com. Running time: 1 hour.