It's not just semantics

THE RULES REVISITED: The difference "between" and the difference "among"

This plot illustrates how a random group of men or women might fall on a masculine-feminine scale – which can be thought of as the combination of a large number of character traits.  Notice that the difference between men and women with respect to the masculinity-femininity scale is actually smaller than the male or female variance on the same scale. Again, the difference among men or women is larger than the difference between them.

If you are thinking about or reading about the differences between the sexes, remember that, in most respects, the difference among is greater than the difference between.