A waffle is a wafer--historically speaking, that is. So is an ice cream cone.
The original wafer was the oblatum, the unleavened Communion wafer (unleavened because the bread at the Last Supper was a matzo). The idea of cooking oblata between sheets of metal to make them as thin as possible goes back at least 1,300 years; a wafer iron has been found at a 7th-century site in Carthage, Tunisia.
In the 13th century, bakers in France and the Netherlands started producing secular versions of oblata with a honeycomb pattern, probably so that there would be no confusion with consecrated wafers. The ice cream cone was originally this kind of wafer rolled into a cornet shape.
The honeycomb pattern proved so popular that the name oblata was largely replaced by wafel or wafer (in French, gaufre), a word meaning “honeycomb.” By the 16th century, the Belgians had developed the deep-dish version of the pattern, used with a leavened batter that we know as the waffle.
The tastiest development of the flat wafer is the Dutch stroopwafel, a large split wafer with a filling of butter and molasses. Unfortunately, true stroopwafels are all but impossible to taste in this country. They don’t have “shelf life” -- the wafers get soggy in a matter of days, and much of the fun is lost.