There are numerous differences between Hawthorne's classic The Scarlet Letter and the movie version. There have been several movie adaptions, but I'm going to assume you mean the most recent 1995 version of the tale.
First, the novel is told by an unknown narrator, but the movie is narrated by Pearl. Remember in the novel, the narrator found the story of the letter in the custom house, and is telling the audience the story.
Also, in the novel we do not see the relationship between Dimmesdale and Hester unfold; it all occurs before the novel begins. When we first meet Hester, she has already had Pearl and is being punished, but in the movie version, we see Dimmesdale and Hester met, fall in love, and commit their affair.
The biggest difference occurs in the end of the movie. At the end of the movie Mistress Hibbins (who has become good friends with Hester) is charged as being and witch and Dimmesdale and Hester are able to escape together and run away to Charleston. In the book Hester and Hibbins are not friends and since Dimmesdale dies after his Election Day Sermon, they do not run away and live Happily Ever After.