Corn flour is another name for cornstarch, which is basically just corn ground into a very fine powder. It is typically used to thicken liquids in cooking.
Note: the two word formation for corn flour is the preferred spelling inside the United States. Outside it is cornflour. Also be aware that cornstarch is a North American term
Cornmeal is also just corn ground into a powder, but this is more coarse and not as fine as corn flour. This is logical since one definition of meal is coarsely ground seeds.
Note: outside the US, cornmeal may sometimes refer to other ground seeds, besides corn. Specifically, in Scotland it may refer to ground oats or oatmeal.
There is also a plant named the cornflower and is known for its vivid blue color. This is also spelled as one word.
They are a round flatbread made from cooked corn flour, grilled by the Garridos — father David and son Christopher — to create a toasty-crisp exterior and cushiony interior. [Detroit Metro Times]
White, powdery cornstarch binds to sebum’s fatty-acid chains through weak electric interactions called van der Waals forces. [Wired]
Week three was coleslaw, and week four was a chocolate blancmange of cornflour and cocoa powder, decorated with tinned mandarins and Dream Topping. [The Guardian]
A variety of breakfast plates come with a tomato-and-onion egg scramble and various sides, including simple black beans, a tomato-shot shredded beef sauté (mechecada), glistening rounds of white cheese and diminutive arepitas – junior versions of the fluffy white cornmeal cakes that are a Gusto Gourmet specialty. [Houston Chronicle]