FX is pushing the 10th season of Ryan Murphy’s “American Horror Story” to next year, the cable channel revealed Tuesday, while announcing its slate of programming through 2021. In other “Ahs” news, FX has placed a series order for Murphy-created spinoff “American Horror Stories,” a “weekly anthology series that will feature a different horror story each episode.”

Along with “Ahs” and its offshoot (which Murphy first teased earlier this month), FX’s roster through the coming year includes freshman series “A Teacher,” “The Old Man,” “Y: The Last Man,” an untitled anthology from B.J. Novak, “A Wilderness of Error,” “Hip Hop Untold,” “Hysterical” and “Pride,” which will join renewed series “Atlanta,” “American Crime Story,” “Archer,” “Better Things,” “Breeders,” “Cake,” “Dave,” “Fargo,” “It’s Always Sunny in Philadelphia,” “Mayans M.C.,” “Mr Inbetween,” “Pose,” “Snowfall,” “The Weekly” and “What We Do in the Shadows.”

FX has not set premiere dates for those series,...