Polenta is made with ordinary cornmeal, as far as I know. Boiled like oatmeal.

Grits are mostly southern. Made of finely ground white corn, boiled also. Hominy is also white corn, just not ground up. I don't like grits, but like to add a bit of hominy to pea soup. Grits are moving into the high class restaurants after being the mainstay of the diets of the very impoverished.