Last time I checked it was a little more complicated than that. I think the Wizarding World is now owned by WB, whereas Harry Potter is where Rowling gets royalties. Thatโs where the distinction between the two lives, which is why there are so many things being spun up lately.
I donโt know how involved she still is but I know back in 2010ish when universal was opening the wizarding world in Orlando they had to run all the design desicisions through Rowling. The park ended up changing the color of the name tags for just the workers in that area of the park because she thought the white on them was to bright.