In the book, we learn that Harry still lives with the Dursleys and has, as always, spent his summer with them. In the movie, we do not get this information. It starts in a restaurant at the train station where Harry gets lucky and arranges himself a date only to be denied by Dumbledore, who comes to pick him up. Poor Harry.
In the private meeting between the Death Eaters, Narcissa Malfoy asks Snape to swear that he will protect her son, Draco. Snape instantly agrees to do it, using the Unbreakable vow. In the movie, it is not Narcissa that suggest doing it, it is Belatrix. Snape also does not agree immediately, but takes a few moments to think about it.
When they are on the train and on their way to Hogwarts, Harry decides it would be a great idea to spy on Draco. He makes a wrong move, unknowingly revealing himself to Draco. When the train stops, Draco petrifies him and covers him back up with the invisibility cloak in hopes that nobody will find him. This is then where the story is different. In the book, Harry is found by Nymphadora Tonks who rescues him and walks him to the gate from where he is then escorted by Snape. In the movie, he is rescued by Luna Lovegood and he walks with her to the gates, from where they use the Thestral pulled carriages to reach the school.
Here is one that did not happen in the book, but is one of the best fear inducing scenes in the movie (in my opinion, of course). When everyone is home over the Christmas break, Harry spends the break with the Weasley family at their home. Just before he gets his first kiss from Ginny they get attacked by the Death Eaters. He follows them out in the field, Ginny behind him and is later joined by others. The Death Eaters used this tactic to draw him out, have some fun with him and as the grand finale, they destroy the Weasley’s home.
Later in the story, Harry once again decides to follow and confront Draco, this time to the bathroom. When he arrives there in the book, he finds Draco talking to the Moaning Myrtle. She also remains there during their fight and lets out a scream, when the fight is over, believing that Draco just died. The Moaning Myrtle, however, does not appear in the movie. It is just the two of them.
After Snape kills Dumbledore and Harry chases him, in the book, there is a battle going on between the Death Eaters and the students and professors at Hogwarts. This does not happen in the movie and the few Death Eaters that were with Snape, run away with him.
Just before Snape makes his escape, he reveals himself as the Half Blood prince. In the book, he explains that he came up with this name, because his mother was a muggle (this means he is only half wizard) and her maiden name was Prince, thus The Half Blood Prince. In the movie, he says that he is the Half Blood Prince, but offers no explanation as to why he calls himself that.
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