The word corn, Wiktionary tells us, can mean:
- (Britain) The main cereal plant grown for its grain in a given region, such as oats in parts of Scotland and Ireland, and wheat or barley in England and Wales.
- (US, Canada, Australia) Maize, a grain crop of the species Zea mays.
- A grain or seed, especially of a cereal crop.
- A small, hard particle.
The word comes through Proto-Germanic from a Proto-IndoEuropean root from which the Latin granum also is derived; the latter gave us the English grain (etymonline). (Maize comes through Spanish from the Taíno word for Zea mays.)
So when the British Colonies in America were settled, corn meant essentially "cereal grain". The settlers found the natives growing Zea mays and called it "Indian corn" (Dictionary of Americanisms). Since it became a major crop of the settlers too, and they already had names for their familiar corns (wheat, rye, oats), the name "Indian corn" was soon shortened in America to simply "corn".
Whether Columbus's voyages returned with maize seed is unclear, but it was soon introduced to the Old World, being one element of the Columbian Exchange, the great transfer of organisms and ideas between the hemispheres which followed the establishment of European travel across the Atlantic Ocean. Columbus was aware of the Taíno cultivation of Zea mays, as there is a description of it from his second voyage in 1494:
It is a grain of very high yield, of the size of the lupine, of the roundness of the chick-pea, and yields a meal ground to a very fine powder; it is ground as is wheat and yields a bread of very good taste. (Histories of Maize)
Adam Smith's reference to corn in ancient times was certainly a reference to cereal grains, perhaps specifically to wheat, but that is not clear.