The corn that grew in Aman is specifically identified as wheat (The Silmarillion speaks of the '...fields and pastures of Yavanna, gold beneath the tall wheat of the gods', in Quenta Silmarillion 8, Of the Darkening of Valinor). Yavanna is also said to have created a particular kind of corn as food for the newly-awakened Elves on their Great Journey, and this was the origin of Waybread or Lembas.

Middle-earth as a whole represents the Old World of Eurasia and Africa in the distant past, so the use of the word 'corn' for maize cannot have applied there (because maize originated in the New World, and wasn't found east of the Great Sea until long afterward). This is not necessarily true of the lands West of the Sea, and indeed The Silmarillion says that '...all living things that are or have been in the Kingdom of Arda ... lived then in the land of Aman...' (Quenta Silmarillion 5, Of Eldamar and the Princes of the Eldalië). That must presumably include all possible kinds of corn, including maize, though only wheat is given a specific mention.