> you could replace every instance of "ball" in this article with "sphere" and it would still be correct.

I completely agree. N-ball is maybe more mathematically precise. It might rule out some strange edge case I couldn't think of. I chose it mostly for stylistic reasons. n-ball is shorter than n-sphere, and ball is a more playful term.

I do however understand the need to define the two object classes, and see little issue with giving them distinct names.