Chemistry of different brands of baking powder
Can anyone say what the chemical difference between the two is?


I can't say definitively. Here are the ingredients of Clabber Girl:


Here are the ingredients of Rumford:



The ingredients are similar, but different ordering. That is significant. Also note that Clabber Girl brand has aluminum as an ingredient, Rumsford does not. 

(I learned from these images that Clabber owns Rumsford brand, I didn't know that)


  Is there a practical difference between different brands of baking powder, or are they all formulated so that they function the same?


In my home baking experience, the brands have been pretty similar. I opine that this is due to competitive and mature markets--you would want your product to be interchangeable with other brands. Few people want to retool recipes to accommodate a rogue baking powder.

Maybe one of the professional bakers here has insights regarding characteristics of different brands.


  Is one of the purposes of filler to make sure that the amount of carbon dioxide per unit of baking powder is the same between different brands of baking powder?


I believe that to be true. The fillers also prevent clumping or caking of the product.



When I first read your Q, I went to look up regulations on Baking Powder content. I didn't find any in the US, which is unusual. Then it occurred to me: Baking Powder invention was well before vigorous food industry regulation. So each brand could do what they want, and still call it Baking Powder.

I also searched patents, and came across this odd formulation:


  ...my invention consists, broadly, in the combination, with the ordinary ingredients of a good baking-powder viz., cream of tartar and an alkaline bicarbonate, mixed in the usual proportions of a small quantity of crystallized saccharine material in a finely-pulverized state. As illustrations of those substances in which this crystallized or crystallizable saccharine material is to be had, I name, first, sugar of milk obtained wholly from milk; second, cane-sugar obtained chiefly in a direct form from the sugar-cane plant, the beet-root, and the sugar-maple, and indirectly from. various other substances by conversion, and, third, grape sugar obtained chiefly from grapes and honey. This latter sugar is, however, not practically available by reason of the difficulty with which it is made to assume the crystalline form. Of these substances the sugar of milk and the cane-sugar are both easily crystallized...


Sugars in Baking Powder?