You will sometimes find coarse masa harina for making tamales, while the more common, finer, masa harina is used for corn tortillas. Both of these are made by treating the corn with cal, a.k.a., slaked lime, or calcium hydroxide, mixed with water, to remove the skin. This process is called nixtamalization, which gives the corn its distinctive flavor and aroma. If you can find some tortillas made immediately from grinding this treated corn up, as opposed to drying the corn, grinding it into masa, and re-hydrating it (how most are made) do try it - they cost more, but they are worth it! The manager at the Mexican grocery/restaurant in town introduced me to these, and lets me k know when he gets them in.
In this country a similar product - hominy - is made, using an even stronger alkali solution - sodium hydroxide, or lye. You will often see this name in hominy grits, though all grits are not treated - you can tell if they are by that aroma, though it's not as strong as in masa harina.
Cornmeal is found in many textures, with the more coarse varieties usually sold as polenta, and the finest as corn, though, as noted above, cornstarch is often called corn flour. In Indian markets I find extremely finely ground yellow cornmeal, even finer than masa, called corn flour, plus other grades, as well.