Both products are whole oats that are rolled, or flattened, but quick oats are chopped into smaller pieces so that they cook more quickly. In many recipes, including this carrot muffin recipe, old fashioned and quick oats are interchangeable. You can use either one. Instant oats and steel cut oats are not suitable for this recipe. Instant oats are rolled even thinner and chopped more finely than quick oats, and aren't suitable for most recipes. Steel cut oats are whole oats that aren't rolled but are cut into thirds. The texture is quite different from either old fashioned or quick oats and they need more cooking time. Try Instant Pot steel cut oats or overnight slow cooker steel cut oats, or even better, carrot cake slow cooker oatmeal.