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The first book in the Harry Potter series and the movie adaptation both have a different title in the United Kingdom. British author J.K. Rowling titled her first book Harry Potter and the Philosopher's Stone, and her British publisher, Bloomsbury Publishing, retained that title. Scholastic later published the book in the U.S., changing the title to Harry Potter and the Sorcerer's Stone, and making other minor changes. When Warner Brothers -- an American company -- bought the movie rights, it kept the American book title.
The Harry Potter in Tayside site quotes Rowling's explanation:

Arthur Levine, my American editor, and I decided that words should be altered only where we felt they would be incomprehensible, even in context, to an American reader... The title change was Arthur's idea initially, because he felt that the British title gave a misleading idea of the subject matter. In England, we discussed several alternative titles and Sorcerer's Stone was my idea.
Other sources offer slightly different reasons for the title change. The Harry Potter Lexicon says, "Scholastic thought that a child wouldn't buy a book with the word 'philosopher' in the title." The U.K.-based Harry Potter Teaching Resources site suggests that the book was retitled "...presumably to make it sound more magic orientated rather than philosophy orientated!"

Perhaps Scholastic doubted that American grade-schoolers would be familiar with the mythic philosopher's stone, a mineral substance that could transform base metal into gold. Alchemists of the Middle Ages sought to discover the stone and attributed many great powers to it.

As a result of the name change, all the scenes in the movie that mention the stone were filmed twice -- once with actors saying "sorcerer's" and once with them saying "philosopher's." Maybe the alternate versions of those scenes will turn up on DVD someday soon.