The sequence of events is different. In the novel, (1) Hannibal's message to Francis is decoded and Will's family leaves Florida (2) then Freddy Lounds interviews Will and gets kidnapped and killed by Francis. In the film, this order is reversed so that the message is decoded after Lounds' death.
In the novel there is the suggestion that Graham deliberately marks Lounds for death by putting his arm around Lounds "like a pet" in the publicity photo; in the film Lounds insists on being in the photo, and puts his arm around Graham.
Francis' backstory that is described in the novel (abandoned by his mother at an orphange, raised by his grandma, killing animals, getting bullied by step-siblings) is completely omitted. His birth date is changed from June 14, 1938 to November 23, 1952. The tattoo of the Great Red Dragon was on his back in the novel.The Freddy Lounds torture scene was originally shot with the tattoo on Tom Noonan's chest, but the scene was refilmed with his shirt on. The blood coming out of Francis' back after the confrontation with Will was to mirror the tattoo.
The scene from the book in which Dollarhyde steals and eats the original Red Dragon painting from the Brooklyn Museum, in an attempt to control the Red Dragon side of his personality, is omitted. In general the whole split personality aspect of the novel is almost absent from the film.
In the novel, Hannibal is both a murderer and a cannibal. In the film, he's just a murderer and his cannibalism is never mentioned.
The final confrontation in the film shows Will Graham going to Francis' home and shooting him to death, saving Reba. In the novel, Francis burns the house and makes Reba think he's dead by having her feel the body of Arnold Lang, a gas station attendant. He later arrives at Will's house in Florida and stabs him in the face. Francis is shot to death by Will's wife Molly, and Will survives. Jack Crawford visits Will in the hospital and destroys a letter that Dr. Lecter had sent to Graham.
Hannibal gets about as much screentime as he appears in the novel, though the telephone conversation with Will was originally a letter he sent to Will.
While the novel takes place in 1980, this film takes place in 1986.