These flours come in various colours such as white, yellow, red and blue. The snack market pays attention to the colours for the desired visual novelty appeal. There are also flavour and texture differences. For instance, blue corn flour has a nuttier taste, and is coarser.
Corn flours can be used as thickeners, though some corn flours will absorb water better than others. Corn that is used for “nixtamalized” (treated with lime) flours tends to be harder corn, hard enough to not break down during the lime-treatment process. The resulting flours are slow to absorb additional moisture, and tend to be used for flours and doughs.
For commercial use, corn flours can be bought “pregelatinized” (already cooked) to cook up faster and blend better. A consumer version of such a flour is masa harina.
Cornflour in the UK and Australia is what North Americans call “corn starch.”
Corn flour (not what Brits call “cornflour”, aka “corn starch”) is milled from the whole kernel of the corn, giving a fine yellow powder that will feel grittier than corn starch. It is a finer grind basically of cornmeal. It is is good for coating items to be deep-fried or fried.
Corn starch is milled from just the starchy endosperm of the corn kernel. It is powdery, very white, and has a silken feel to it. It can be easily confused visually (though not by taste) with icing sugar (aka powdered sugar.) It is used as a thickener.
The confusion between cornflour (the starch) and corn flour (the flour) doesn’t arise much in Britain, if only because you can barely find corn meal there, let alone the finer grind that North Americans call corn flour.