Answer :
It depends on what adaptations you're looking at but I'd say some significant differences across the board are the portrayals of the monster. In the books, the monster can speak eloquently and read as well while he mostly grunts and struggles with words in the movie adaptations.
In the book, the monster mostly behaves like a human while it looks like a monster, while the movies want to make it even more of a horror story so they make him make noises or speak incoherently and rumble and growl and similar things. The idea behind it in the books was to show that he could be more human than the real human who made him.