No, the different types of oatmeal are not at all the same in terms of nutrition. The very outermost portion of the oat (called the hull) is always removed before the oat is eaten. However, once the hull has been removed, there are several further processing steps that can be taken. Because these additional processing steps almost always serve to lower the nutritional value of the oats, I recommend the least number of additional processing steps to give yourself the best nourishment possible from your oats. The least processed forms for oats are oat groats and steel-cut oats. Oat groats consist of the hulled but unflattened and unchopped oat kernels. Steel-cut oats are the same as oat groats, except for being chopped with steel blades. Because they are the least processed, these two forms of oats are also the most nutritious.
Old-fashioned oats are chopped, steamed, and rolled to give them their flatter shape. Because they are more processed, they are less nourishing than oat groats or steel-cut oats. However, they are still better sources of nourishment than most quick-cooking oats or instant oatmeals. Quick and instant oatmeal usually have their oat bran—the layer of the grain that's just beneath the hull—removed. Many vitamins and much of the oat's fiber are contained within the bran, and so its removal is particularly problematic when it comes to nutritional value. Oat groats, steel-cut oats, and, to a slightly lesser extent, old-fashioned or rolled oats would be your best choices here, with quick and instant oatmeal usually being less nourishing due to further processing and the removal of their bran.