They are different.
When oats are processed, the hulls are removed and then they are steamed, then cut or rolled. The outer layer of the oat (like most grains) is called "bran." Sometimes the bran layer is removed and processed separately to make a product called "oat bran." You can buy it at health food stores, etc.
Most oatmeals, including quick and instant, contain whole oats, so that means that the whole grain, including the bran is included.
Regaring your recipe .... I am not positive, but since instant oatmeal is usually oatmeal that has been cut up into fine pieces, you probably should be able to use it.
But maybe someone else can alswer that more accurately.