The Brits are more innovative when it comes to new structures. American English sticks to ancient norms such as the Germanic noun tendency to compound nouns. E.g.
Schornsteinfeger, chimneysweep, boatswain, bookcase, weekend. The norm here has always been to compound nouns in the singular. While German still writes them as single words, they are spoken in
AmE as though they were one word. Example: on the
weekend (US), vs at the week
end (UK); this indicates they are separately constructed in
BrE (cf.
at the end of the week, the week's end, the week end).
So
AmE naturally prefers the term "drug trade" whereas the Brits have begun to lose this preference, and will often write "drugs trade" by virtue of common sense, rather than tradition.