The book, which is set in the 1800s when it was written, sees the governess — who remains unnamed — moving to Bly to take care of the orphaned children, Miles and Flora. The uncle in both stories is uninterested in raising or hearing about the kids, although we learn more about why in Bly Manor.
While Miles has already been expelled at the start of show, in the book only Flora is at home to begin with and Miles returns home a little later, after being expelled from boarding school.
While Dani clearly feels affectionate and protective towards Miles and Flora in the show, the book's governess is much more attached to them, and to Miles in particular. Like, unhealthily obsessed.
In fact, The Turn of the Screw is not so much an explicit ghost story as it is a mystery centred around a young woman's mental unravelling. Whether the ghosts are real or a symbol of the governess's mental state is left open to interpretation, which makes it all the more chilling.
Interestingly, this is similar to The Haunting of Hill House. While the show makes the ghosts very real and part of the story, the original book is much more ambiguous, and there's a strong argument that Nell's mental state, and not ghosts, is the real problem.