Griddle, grill, and gridiron all ultimately derive from the same root (Online Etymology Dictionary):
cooking utensil, early 14c., griderne, alteration (by association with iron) of gridire (late 13c.), a variant of gridil (see griddle). Confusion of “l” and “r” was common in Norman dialect. Also a medieval instrument of torture by fire. As the word for a U.S. football field, by 1896, for its lines.
shallow frying pan, early 13c., apparently from Anglo-French gridil, Old North French gredil, altered from Old French graille, from Latin craticula (see grill).
“gridiron,” 1680s, from French gril, from Old French greil, alteration of graille “grill, frating, railings, fencing,” from Latin craticula “gridiron, small griddle,” diminutive of cratis “wickerwork,” perhaps from PIE *kert- “to turn, entwine.” In many instances, Modern English grill is a shortened form of grille, such as “chrome front of an automobile.”
Grilling is a cooking method that uses any of these devices to apply dry heat to the surface of food (Wikipedia):
Food to be grilled is cooked on a grill (an open wire grid such as a gridiron with a heat source above or below), a grill pan (similar to a frying pan, but with raised ridges to mimic the wires of an open grill), or griddle (a flat plate heated from below).
While a grill (n.) is usually a device with a wire rack, raised ribs, or similar grid pattern, there are exceptions like the flattop grill that have a flat surface like a griddle. And we can grill (v.) food on a griddle,* because the cooking method is essentially the same regardless of the surface you use. Or to put it another way: The verb for grilling hasn’t become as specialized as the names of the grilling tools, and the adjective grilled comes from its participle.
* Yes, you can griddle (v.) food too, but it’s a very uncommon usage.