A question sort of about a recipe: Polenta with Wilted Escarole and Olive Oil Fried Eggs

I have a question sort of about step 1 on the recipe "Polenta with Wilted Escarole and Olive Oil Fried Eggs" from merrill. It says:

"Combine the polenta, milk, 1 1/2 cups cold water and 1/2 teaspoon salt in a medium saucepan. Bring to a boil over high heat, whisking frequently. Reduce the heat to low and cover the pot. Let the polenta simmer, whisking every few minutes to make sure it doesn't clump, for 10 to 15 minutes, until it's thick and creamy and tender to the bite. Once the polenta is cooked, taste for seasoning and add salt and black pepper to taste. Turn off the heat and keep covered in a warm place."

I am confused about cooking times for polenta In many recipes it says 15 minutes or so as demonstrated above. In articles or other places it says to make real polenta it needs to be cooked for three hours or much longer than 15 minutes. Does it really make a difference cooking it that much longer or is it a special kind of cornmeal/polenta that makes it necessary to cook it for so long?