Does anyone know what the true first of Gaiman's "American Gods" is?
I see that both US and UK editions came out in 2001. A search on
abebooks.com did not shed any light on this issue, as both editions
were offered as "firsts."

The U.S. edition precedes by a few weeks.

For future reference, the best group to ask such questions in is
rec.collecting.books (to which this reply has been copied).