Here's a breakdown:
* The books and movies are fictional: The wizarding world of Harry Potter exists solely in the imagination of J.K. Rowling. It's not a real place.
* Universal Studios created a theme park: Universal Studios, a real-world theme park, decided to create a themed area based on the Harry Potter franchise. They bought the rights from Warner Bros. (who owns the film rights) and built the attractions.
* The Wizarding World is an attraction: The Wizarding World of Harry Potter is a themed area within Universal Studios. It's not the actual wizarding world from the books and movies, but a highly detailed and immersive recreation.
So, to summarize, the wizarding world of Harry Potter didn't "move" to Universal Studios. It was created there as a theme park attraction.