I have a receipt from Publix that says I saved $4.35 on my last purchase. What does that mean? Do I possess $4.35 more than I would without those savings? Probably not; I wouldn't have bought five microwave meals if there wasn't a handy five-for-$10 sale going on.
Did I, then, acquire $24.35 worth of goods and only have to pay $20.00 for them? This, I think is closer to the mark. Publix, however, got more than money from me. By buying items on clearance, I probably cooperated with the manager's inventory plans. I assume that discounts are used to guide what people buy and I'm generally happy to follow these guidelines in exchange for lower prices.
In any case, the world of digital sales has probably spoiled me a bit when it comes to 'savings.' When I'm buying a discounted computer game, I only consider it a good deal if it's 75% off or more.