For many recipes, it is perfectly fine to substitute oil for shortening or, inversely, to melt shortening and substitute it for oil. Some foods, including many baked goods and cookies, cannot be made using oil as a substitute for shortening because it alters the texture of the food.
Shortening is a solid fat, and when it is beaten into batter, air is added to the mixture. The result is a lighter cake-like structure for baked goods. If oil is substituted, the texture will be denser and not as airy. Recipes using shortening tend to create a tender, light crumb. Cookies can often take either, making them a good choice for experimenting.