There are only 2 Harvest Festival-only items, the Cornucopia and the Fruit Basket. But first, I must explain.
Franklin will ask you to make 4 recipes - a salad, a soup, a main course, and a dessert. He will tell you 3 ingredients, but there is a 4th secret ingredient. You can get a hint as to what that is from your villagers that are dressed as chefs, after you give them the fish they are asking for. Giving them a fish is also how you get butter, flour, and other ingredients that you can't normally get.
The first dish that you successfully make with all 4 ingredients, to include the correct secret ingredient, gets you a fruit basket. If you get all 4 dishes correct with all of their ingredients, you will get a cornucopia. Every other time, you'll get a Harvest set item (same ones you can buy from the Nookling store). I'm not sure what happens if you get the wrong secret ingredient. You might get just a Harvest set item for that too.