When I worked at USDA in the small grains lab, we did not include corn because there were so many varieties. It had it's own lab (as did rice). There are an amaizing (oh, look, a pun) number of varieties of corn, and a rainbow of colors. Several years back the Smithsonian had an exhibit.
Here's an interesting link:
Here's a list of the kinds of sweetcorn:
And a list of types of corn:
Many forms of maize are used for food, sometimes classified as various subspecies related to the amount of starch each had:
Flour corn — Zea mays var. amylacea
Popcorn — Zea mays var. everta
Dent corn — Zea mays var. indentata
Flint corn — Zea mays var. indurata
Sweet corn — Zea mays var. saccharata and Zea mays var. rugosa
Waxy corn — Zea mays var. ceratina
Amylomaize — Zea mays
Pod corn — Zea mays var. tunicata Larrañaga ex A. St. Hil.
Striped maize — Zea mays var. japonica