"Corn on the cob" was a term used to refer to an ear of freshly-picked corn that was cooked and served as food, with the corn kernels typically being eaten right off the cob. A platter full of corn on the cob was one of the dishes served at the Welcoming Feast at Hogwarts School of Witchcraft and Wizardry in 1991.
Popcorn was a unique variety of corn which had hard kernels that swelled and burst open when heated. It was a popular snack food consumed by Muggles and wizards alike, usually being served with salt, butter, or other seasonings. "Buttered popcorn" was one of the many different flavours of Bertie Bott's Every Flavour Beans.