Yes, the Shawshank State Penitentiary featured in the show is the same as the title facility in the 1994 film The Shawshank Redemption, which is based on a story in King's 1982 novella collection Different Seasons. In fact, the character of Red — played by Morgan Freeman in the big-screen adaptation — is from the town of Castle Rock. Mentions of the prison can also be found in It, Bag of Bones, Dolores Claiborne, and a handful of other stories. In the show, the prison is presided over by the late warden Dale Lacy (Terry O'Quinn) just before the events of the series begin, and it's where Bill Skarsgard's mysterious character is first discovered.