The better comparison is probably with Percy Jackson, which isn't quite the same concept (being an American series, where boarding school fiction isn't quite as well-known a genre) but matches the ages, sense of discovery, and relationships to authority figures far better.
This isn't directly relevant to your point, but I really find it wild that people see two stories that have magic and a school in them and go "look, it's the same thing", especially when the genres and tropes of the two books are so utterly different. For that matter, Harry Potter is also nothing like Earthsea, which is another common reference point. I wonder if Americans just don't have as much experience with boarding school fiction to be able to categorise Harry Potter as a series?