In the US, the white powdered starch used in cooking is called cornstarch. But "cornflour" in Australia is US "cornstarch" and in the US cornstarch is made from corn while in Australia it is made from wheat. The grain it is made from probably doesn't matter because it is simply a thickening agent and adds no flavor etc?? An American cooking in Australia might think that cornflour is finely ground corn but ground corn (US "cornmeal") is called polenta and is usually roughly ground. I haven't seen any finely ground corn in Australia, what I would call "corn flour".Wikipedia entry on cornflour - Cornflour is an ambiguous term that can mean cornstarch or finely ground cornmeal.

This comparison of US vs UK vs Australia vs Canada terms is from
US cornstarch
Canada cornstarch
UK cornflour
Australia cornflour (see note)
Note: Cornflour (Australia) - In Australia (and New Zealand?), cornflour is frequently made from wheat. FSANZ regulations require such cornflour to declare that it contains wheat and gluten, and it is usually described as wheaten cornflour. There are some brands of cornflour that are made from maize, however.
I checked this and the Woolworths (Australian supermarket) brand of "cornflour" is called "wheaten cornflour" and is made from wheat.

Wikipedia entry - Cornstarch is a starch made from corn. It is not to be confused with cornmeal or corn masa. Both cornstarch and finely-ground cornmeal are sometimes called cornflour; this is thus a bad term to use.

Why this confusion? Corn is the new name for maize (probably adopted by us Americans to confuse the British). Whereas corn used to be the English term for any cereal grain.

More from wikipedia on cornstarch -
Cornstarch is commonly used to thicken sauces. Commonly, anywhere from 1 t to 2 T of cornstarch are added to 1 c of fluid. The mixture must be boiled to activate the cornstarch. When a recipe uses cornstarch in this way, you can often substitute one of xanthan gum, pectin, agar, or gelatin.
Cornstarch can be applied to wet items, drying them off so that batter will stick. This is commonly done for deep-fat frying. When a recipe uses cornstarch in this way, you can often substitute flour or cornmeal.
Cornstarch may be added to powdered sugar to prevent clumping.