Although Morgan Freeman doesn’t look anything like his novella counterpart, you’ll have a hard time finding anyone who doesn’t think he did a good job here. As has been widely acknowledged by this point, Freeman’s got a voice made for narration; even if you hate voiceovers in movies, he’ll manage to win you over within just a couple minutes.
The movie also benefits from the greater suspension of disbelief afforded by the medium. While most of the same basic plot points happen in the novella, you can see Stephen King struggling at times to explain how Red knows about so much of what’s going on with Andy in each part of the story. It’s written specifically from Red’s first-person point of view, after all. The film, meanwhile, is not as closely tied to Red’s perspective, and Freeman’s charisma in the voiceovers helps to smooth things over, preventing the viewer from getting too wrapped up in figuring out how and why Red knows about this or that.
Looking back at it today, there are some clear lessons to learn about casting in adaptations. One of the more recent controversies has been the online anger about Bella Ramsey being cast as Ellie in “The Last of Us,” despite the fact that she looks different from the videogame character. It’s nothing new; every time an adaptation bases its casting choices on something other than looks, fans of the source material aren’t happy. But as Morgan Freeman made abundantly clear in “The Shawshank Redemption,” finding an actor that captures the spirit of the character, not their exact facial features, is most important.