You're not entirely incorrect but prom in western school stuff is just the festival stuff you see in anime but culturally relevant. It's the same thing, an experience most people have in junior high or high school that people can relate with but it's not just an anime thing it's a Japanese culture thing. The school sports festival is probably similarly experienced, a thing that happened when you were a kid in school but you didn't think that much of it, but you do know it's a thing that happens to almost everyone.