I have read the story and have seen the movie version. The movie and the story are very similar, except for some major main points; which was based on how Beowulf deals with Grendel’s mother, where he becomes king and who the dragon and Grendel really are.
It was stated in the book that Beowulf, after defeating Grendel’s mother (by a sword made by giants) he goes back to Geatland after victory to become king of his uncle Edgetho kingdom. Beowulf had cut Grendel’s mothers head off, and he showed it to all the people in Hrothgars kingdom Herot. So there it was believed that he accomplished and proved his bravery of defeating her. In the movie, Hrothgar is accused of cheating on Welthow with Grendel’s mother and giving birth to Grendel.