As with any film adaptation, there are differences from the novel. As was the case with the previous two Harry Potter movies, the time between events is often compressed as compared with the book, scenes and dialogues from the book are shortened or combined, and some scenes placed elsewhere in the narrative. Beginning with this film, the Harry Potter films begin to take more liberties, make more adjustments, and more cuts into (subplots of) the story. For example: the previous films showed Harry in almost all of his classes, whereas this movie has relatively few of such scenes. The following lists describes the largest deviations from the plot:
In the novel, Harry celebrates his birthday alone at the Dursleys' house. After a failed attempt to congratulate Harry by telephone, Ron and Hermione send him presents by owl post. Ron gives Harry a Sneakoscope, a device that warns the owner when an untrustworthy person is in the vicinity, and announces that he and his entire family have won money in a contest, and are going on a holiday to Egypt.
Aunt Marge stays for an entire week, annoying Harry with her concescendance. Harry assumes the name of his classmate Neville Longbottom when he is on the Knight Bus. There he learns that Sirius Black was convicted of killing 13 people with a single curse. Harry tries to get Cornelius Fudge to sign his permission slip to enter Hogsmeade, but Fudge refuses.
Harry spends some days at the Leaky Cauldron, where he learns that seeing a large black dog is an omen of death. His classmates arrive, and Hermione buys Crookshanks in a pet shop after the cat tries to attack Ron's pet rat Scabbers. In the train, Harry's Sneakoscope already starts to alarm, but they dismiss the device as defective (Actually it picks up on Scabbers, who is later revealed to be Peter Pettigrew in his Animagus form). The memory that Harry relives each time a Dementor is close becomes much more detailed with every iteration: he can clearly hear both his parents' final words before they are murdered. During the trip from the train to Hogwarts, Ron and Harry notice that the carriages are pulled by something invisible (explained in Harry Potter and the Order of the Phoenix). At Hogwarts, McGonagall shows concern for Harry's health after the Dementor incident, but he dismisses her wish for him to be admitted to the hospital wing.
The novel gives descriptions of each of Harry's classes, all the way up to final exams. This has been cut down a great deal in this film, so that we merely get an introduction to each of Harry's new teachers: Hagrid, Trelawney, and Lupin. Professor McGonagall immediately dismisses Trelawney's powers, as the latter has mistakenly predicted an impending death several times. There are several Hippogriffs shown during Hagrid's lesson. After the lesson, Harry, Ron and Hermione find Hagrid drunk and miserable, convinced that the incident with Draco and Buckbeak will get him sacked; his classes become much less fun afterwards.
As Harry isn't allowed into Hogsmeade, Lupin invites him for tea. The Lupin in the movie makes it clear that he knew Harry's mother, something only hinted at in the book. Snape enters and hands Lupin a potion, which he subsequently drinks, despite Harry's objections. The Fat Lady goes missing for several days after Sirius Black attacks her portrait; sir Cadogan, an inept knight, takes her place at the entry of the Gryffindor common room. Following the incident, Harry notices that all teachers start to get extremely protective of him.
Quidditch, a highlight of the previous films, gets only a cameo appearance in the movie. Harry is shown in only the first game against Hufflepuff, which incidentally introduces their new Seeker, Cedric Diggory, in the book. The book features the two subsequent games as well, after which Gryffindor, for the first time in years, wins the Quidditch cup (they lost it in the previous books because Harry was hospitalized (Philosopher's Stone) or the game itself had been suspended (Chamber of Secrets)). The second match incidentally introduces Cho Chang, Ravenclaw's new Seeker (as well as an important character in the next two books).
Two of Harry's unauthorized visits to Hogsmeade are combined in the film. During the first, Harry (hiding underneath a table to avoid being seen), Ron and Hermione overhear Cornelius Fudge talking to a few Hogwarts Professors about Sirius being Harry's godfather, James and Lily Potter's friend, as well as their Secret-Keeper; the latter role involved a complex spell, causing the Potter family's secret location to be completely invisible to anyone but Black and to those he disclosed the information to. Since Voldemort knew exactly where to find the Potters, this is considered proof that Black betrayed them to Voldemort. Apparently, Peter Pettigrew had confronted Black with this, only to be killed by Black together with 12 innocent Muggles, earning him a life sentence in Azkaban. In the film Harry heard the conversation by himself while under the Invisibility Cloak.
Harry is consumed with rage over this news, that was apparently withheld from him for years. He plans on confronting Hagrid about it, but Hagrid is in tears over the news that Buckbeak is likely to be executed following the incident with Draco. Harry calms down and promises to see if they can find legal grounds to get Buckbeak exonerated.
A Christmas dinner is organised for the teachers and students who remain at Hogwarts over the holidays. Ron and Harry learn that Lupin is 'sick' again and receives Snape's potions regularly. The Quidditch subplot also introduces Harry's new broom, the Firebolt, much earlier in the story. Harry actually receives the new broom before dinner, and Hermione immediately (and correctly) guesses that Sirius Black sent it. That there appears to be nothing wrong with it may be Rowling's first hint that Black is not the villain he's been made out to be. Unfortunately, the teachers find it highly suspicious, and immediately confiscate it for thorough examination, taking weeks before Harry gets it back. Ron and Harry are furious with Hermione, who apparently warned the teachers about the broom.
This, and the Marauder's Map (especially its shady origins and potential danger) causes the boys' relationship with a sceptic Hermione to cool down significantly. It is worsened by the increasing tension between Ron and Hermione over Crookshanks, who keeps targeting Scabbers. During one of these attacks, Harry's Sneakoscope sounds, another ignored hint that someone (in this case Scabbers) is not what he seems to be. A bloody sheet with Crookshanks' hairs on it temporarily ends their friendship. While this subplot is mainly cut from the film, some of Ron and Hermione's initial arguments were used, though they were not as serious compared to the book.
Harry has several unsuccessful lessons with Lupin in mastering the Patronus charm. During one, he learns that Lupin started at Hogwarts in the same class as Sirius Black, and that the Womping Willow was planted in their first year. Harry finally succeeds with the Patronus when the Dementors again show up during the second Quidditch match; however, these 'Dementors' are quickly revealed to be Draco and his friends in disguise, in an attempt to scare Harry into losing the match. That same night, there is another 'attack' by Sirius Black, directed at Ron's bed; Black apparently found a list of passwords for the dormitory that was lost by Neville (who receives severe punishment).
During Harry's second secret visit to Hogsmeade, the invisible Harry throws mud at Malfoy, Crabbe and Goyle, resulting in Malfoy seeing Harry's head and reporting him to Snape, who catches Harry sneaking back into school. Before Snape confiscates the map and gives it to Lupin, Harry confronts Snape with a rumour he heard in his first year, namely that Snape resented Harry's dad due to a life debt. Snape retorts that James once put him in considerable danger, but saved him, not out of care for Snape's life but of fear for getting expelled. In the movie, Harry throws snowballs at Draco and his cronies at Hogsmeade and Harry loses the Map to Snape when the latter catches him looking for Peter Pettigrew (which is not in the book) instead since Draco did not find out that Harry was in Hogsmeade illegally in the movie, though like in the book Lupin does take the Map into his possession.
Buckbeak's sentence and Hermione punching Draco in the face occur much earlier in the book, which brings the trio back together and renews their friendship. During final exams, a final appeal for Buckbeak is scheduled at school, but since this is also the day of his execution, the appeal is mainly a futile formality. Despite Hagrid urging them to stay away, the three use Harry's Invisibility Cloak to comfort him. In Hagrid's hut, they find Scabbers hiding (in the movie, Hagrid had found him).
During the confrontation with Sirius Black, Lupin mentions he followed Black to the Shrieking Shack with the Marauder's Map; this is also how he identified Scabbers as the supposedly deceased Peter Pettigrew. The novel also goes into more detail about Sirius' and Lupin's backstory: the Shrieking Shack was actually built to house Lupin as a student, each month as he transformed at the full moon. The Whomping Willow was planted to protect the underground entrance to the Shack, with a special trick to avoid the tree's branches. His friends, James Potter, Peter Pettigrew and Sirius Black all became Animagi (adopting the nicknames Prongs, Wormtail and Padfoot), so they could accompany Lupin ('Moony') when he transformed. Together they also created the Marauder's Map. Sirius decided to play a cruel and dangerous trick on an already suspicious Snape by telling him that he could find out Lupin's secret by going to the Whomping Willow. James, knowing Snape could be killed if he met the Werewolf, kept Snape from doing it. Snape still figured out that Lupin was a werewolf, and remains convinced to this day that James only warned him to save himself and Sirius from expulsion. With Snape's potion, Lupin is now able to undergo the transformations while retaining his human mind, rendering him harmless and suitable to teach (but in the excitement over Peter Pettigrew, he forgot to take his current dose).
Pettigrew's backstory is more elaborate: Sirius had suggested to make Pettigrew the new Secret-Keeper, and then found out that Pettigrew had betrayed the Potters. Sirius cornered Pettigrew, but the latter fired the Curse that killed 12 Muggles, and faked his death by cutting his own finger and escaping in rat form during the mayhem. Sirius was innocently sentenced to death, but felt guilty anyway, because he had suggested Pettigrew as the new Secret-Keeper. He kept himself sane by turning into his dog form regularly, a state in which the Dementors affected him much less. But when he saw a newspaper with a picture of the Weasley family after winning their contest, he recognized Scabbers and escaped. He stayed around Hogwarts, even being helped inside by Crookshanks (who stole Neville's password list), the only one who also recognized Scabbers as a fake. Pettigrew again faked his death and hid in Hagrid's cabin. After returning to human form, Pettigrew denies everything and still tries to put the blame on Black, but his lies are easily disproven. He is scared to death to go to Azkaban, mostly because he was the one to send Voldemort to his unexpected demise, and therefore fears the wrath of the remaining Death Eaters.
Hermione is present and affected during the Dementor attack on Harry and Sirius. In the film Hermione stays with Ron after he is knocked out. The Dementors try to perform the Kiss on Harry as well. In the hospital wing, no one believes Harry's story since Snape claims that Black had used a Confundus charm on him, and Cornelius Fudge is all too willing to believe this easy explanation rather than admitting that Black was innocent all those years. Later, Snape goes as far as accusing Harry of helping Sirius escape, but he has no proof of this.
When traveling back in time during the events of saving Sirius Black, Harry and Hermione, after rescuing Buckbeak and watching the events unfold in the Forbidden Forest decide to head back to Hagrid's empty cabin (due to Hagrid heading up to the castle with everyone else after the execution failed for some drinks) due to the transformed Lupin hanging about until it was safe to return to the Forest. When Harry goes on to scout ahead he realizes the one who conjured the Patronus that saved his past self was him and not his father. In the film this is drastically altered where the transformed Lupin tries to attack them after Hermione does a fake howl to draw him away from their past selves and Buckbeak fights off Lupin and forces him to retreat. Hermione was also with Harry when he performed the Patronus as well as convincing him that no one was coming when Harry was still under the impression his father was going to save them.
Harry's final talk with Lupin in the movie is a mix of two conversations in the book, with Lupin and Dumbledore respectively. Dumbledore also notes that Professor Trelawney had actually made a correct prediction, which happened only once before (an allusion to a revelation in Harry Potter and the Order of the Phoenix). He also mentions that Pettigrew now owes Harry a life debt, since Harry prevented Sirius from killing him (becomes an important point in Harry Potter and the Deathly Hallows).
Everybody passes the exams at the end of school year, and Gryffindor wins the House Cup, largely due to winning the Quidditch games. Hermione has dropped a few subjects and got rid of her Time-Turner. During the train ride home, Harry gets a package from Sirius, containing a signed Hogsmeade permission. The owl delivering the message is for Ron, since Ron no longer has a pet anymore. After arriving at the station, Harry entrusts uncle Vernon that he has a homicidal godfather, hoping it will scare the Dursleys into treating him better.