Grits are thicker version of cornmeal
Cornmeal
Cornmeal is dried corn that has been ground. It is coarser than flour, but retains a slightly grainy texture, as well as a powdery quality.
Different grinds are available – fine, medium, coarse – depending on the application.
Varieties derived from white, yellow and blue corn are available.
Common uses: In cornbread or corn cakes (griddle cakes or ho cakes), to coat baking surfaces for French or Italian bread loaves and pizza crusts (to prevent sticking), in batters for some fried foods (to add crunch and flavor).
Grits
Grits are similar to cornmeal. They are made from dried and ground corn, but are usually a coarser grind.
Grits are often made from hominy (corn treated with lime or another alkaline agent to remove the hull).
You may hear corn used to make grits referred to as “dent” corn. This is because of the indentation left in the corn kernel after drying. The starch in dent corn causes grits to cook to a thick, creamy consistency.
Varieties: Stone ground (whole grain and retain the germ and all of its nutrients; these take longer to cook, nearly 1 hour) or instant (processed and partially cooked prior to drying, these are less nutritious but take less time to cook, usually only 5 minutes or less)are most common.
Common uses: As a breakfast dish (buttered grits or cheese grits) or as a side dish or accompaniment to other meals (Shrimp and Grits). Meats such as cooked ham or bacon are also sometimes added to grits, or they may be topped with the Southern delicacy, Red Eye Gravy.
http://www.glutenfreegigi.com/the-difference-between-cornmeal-grits-and-polenta/