Are most "store brand" items made by the "name brand" manufacturer?

WalMart has its own food brand(Great Value). Most of their store-brand food items are hard to distinguish from the brand names. Question: Since WalMart does not build a factory just to make their own store brand of foods, is the packaging and name the only difference or does WalMart have their own specifications for food items, like canned soup? Their current promo is to reduce the sodium content in many canned items, so how does WalMart accompish this?