Most of the differences between the English of the UK (which we shall call BrE) and the English of North America (which we shall call AmE) are vocabulary differences and differences in pronunciation and spelling. However, there are some differences in the way grammar is used. Almost all of the structures in this book are used in both varieties, but there are often differences in how common a structure is in one variety or the other. There are fewer differences in writing than in speaking.
Does "both varieties" refer to BrE and AmE? If yes, they are varieties of what?
Does this mean the same thing?
... Almost all of the structures in this book are used in both BrE and AmE ...