Is there REALLY a difference in powdered milk brands for baking bread
There are some differences between powdered milk brands -- most significant is in if they have fat in them or not.  Most powdered milk are non-fat, but there are a few such as Nido that contain fat in them.

Your recipe specifically says nonfat powdered milk, so it significantly reduces the differences.  There might be some variety because of how they're produced (vaccuum only, vaccuum plus mild heat to dry it) or what the source of the non-fat was (eg, if it came from butter-making).

There are also come companies that fortify (add vitamins) to their powdered milk -- Nido again comes to mind.  Some of the vitamins (eg, vitamin C) can make a difference in yeast activity.

That being said, the majority of times when a recipe calls for a specific brand**, it's because the recipe was distributed by a specific company, and they're trying to get you to use their brands. Pillsbury, Kraft and Campbells are quite common in this regard, and I wouldn't be surprised if other companies did so as well.

** Except in the case of hot sauces.  Although there are some hot sauce cookbooks distributed by Tobasco and such, the differences in heat and spicing are quite significant, and some cookbooks will say things like "1 TB hot sauce (such as Frank's Red Hot)".

My personal recommendation would be to try to look up the nutrition information for the variety they call for, and the one you have.  If they're similar (same amount to reconstitute to a cup of milk, and similar sugar levels), I'd go ahead and try it -- you might even like it better with the different brand.  If it doesn't come out quite like you're looking for, then go ahead and try to find the specific brand from the recipe.