At the final stage of checkout on your Web Store, your buyers are presented with a list of available shipping methods for their order, which might look something like this:
Shipping methods work by calculating rates for all methods you offer, then grouping them by shipping type (speed), then showing the cheapest method of each type on the checkout page. The buyer is never shown the name of the carrier or the specific method; just the speed. Because of this, you can decide on your end how to ship the order, and aren't necessarily tied to the method the buyer selected on checkout!
A buyer chooses "Standard" shipping on checkout and pays $18. You know per your shipping settings that "Standard" corresponds with "UPS Ground," which means the amount she paid came from that method's quote.
When you process the order and generate the shipping label, you notice that UPS Ground would cost you $16 to ship, but USPS Priority would only cost $13, and would be delivered to the buyer around the same time. In this case, since you never specified the carrier or specific shipping method to the buyer on checkout, the buyer doesn't have any expectations for the package. Because of this, you can choose to use USPS Priority (or whatever comparable method you want) to save money on the package.
As a followup thought, if the price difference between what the buyer paid and what you'll pay is large enough, you could take it a step further and refund a portion of the buyer's shipping cost to provide a mind blowing customer experience. Even if it's just a few dollars, handing a small refund back to the buyer could work wonders for your reputation!