Difference between old fashioned and quick oats?
Old fashioned oats are rolled whole-grain oat kernels. In quick oats, on the other hand, the oat kernel is first cut into smaller pieces before being rolled. This makes it much easier for quick oats to absorb water than an old fashioned oat. You can visibly see the size difference.

For baking quick oats can be used in place of old fashioned oats. However, if a recipe calls for quick oats, you may not get expected results using old fashioned oats. Typically, a recipe that calls explicitly for quick oats generally has too short a cooking time for regular oats to fully cook (e.g. pancakes).

Another thing altogether is instant oats. Do not substitute these in any recipe. Instant oats are parboiled, dried, and often has sugar and salt added.

Nutritionally, quick and old-fashioned oats are identical.