Both are ground corn (maize, as they would have it in Europe). The difference is that corn flour is usually ground to a much finer texture than cornmeal.
While in some contexts (such as breading chicken), they can both be used, you will get different textural results. In general, you want to use the right product.
For example, corn muffins are normally made with corm meal, and if made with corn flour, would be much denser and without the mouthfeel the individual cornmeal granuals provide.
Update: in some places, polenta is another term for corn meal (as well as for the porridge or mush made from the corn meal).
Masa is dried lye-treated corn, which has been ground. It is used widely in southwestern, central, and south American cuisines, including for the iconic corn tortillas, and for tamales.