Maize is also commonly known as Corn. Corn and maize are the same thing, however there are different varieties of corn, including the vegetable Sweet Corn (or corn-on-the-cob).
When the grain is dried, it can be milled in to flours, or heated to create popcorn and breakfast cereal. Also, corn starch is used in cooking to thicken sauces. In the UK, it is confusingly called cornflour, though technically it's not a flour at all.