There are hundreds of kinds of boxwood. I'm only talking about one kind.

Dwarf box on the left, tree box on the right. One dwarf must have died and been replaced by a tree box. Very interesting. Oakwood Cemetery, Raleigh 2025

American boxwood, Korean boxwood, Japanese boxwood.... English boxwood. Very confusing, but if we boil it down to the most common box grown in gardens for most of history, it's American or English. But there's no such thing. Both originated in southern Europe and the Caucasus, and the English brought them to North America. In England, English box is called dwarf box, and American box certainly isn't called that. So it's better to use these names: Tree box (instead of American box) for the one that grows much taller, faster, and more open like a normal shrubby tree. This is Buxus sempervirens 'Arborescens' (evergreen treelike box)

Dwarf box (instead of English box) for the one I'm passionate about, that grows excruciatingly slowly (1" per year), has smaller leaves packed very tightly, and has an aroma. This is the one historically used for parterres and knot gardens because crisp edges can be formed and remain for a whole season. This is Buxus sempervirens 'Suffruticosa' (evergreen shrublike box)