That isn’t saving money it’s spending less money as I see it. If you took the surplus amount you would have spent and put that in a long term investment or savings account then I think you could claim a savings. Almost no one does this with day to day spending though so it’s best to view it as spending less. When you spend money you aren’t saving money. You are spending it. You might be spending less in a given situation than you would have if the circumstances were different but it isn’t a savings.

You wouldn't see the following statement as correct usage? "I was going to run to [store x], but I wanted to see the new [store y] instead and it ended up saving me $[amount]."

I'd agree that a "savings" figure on a receipt is bogus though, as it's comparing a price you wouldn't be charged with one you would.

In our everyday speech this is how people talk. So in that sense it is correct usage. I claim it is misleading to think this way. I think our speech has been affected by marketing and it’s caused a change in how we think about money.

Spending money is never a savings. All you can do is spend less than what you were willing to spend. I know our way of speaking isn’t going to change anytime soon but I hope to change the way people think about saving. I hear people who are broke talk about how much they saved in the scenario you presented. But they have no savings at all and it is bad for them to think they saved money when in fact they spent money. Spent money is not a savings.