Paying abroad often produces a choice between the local currency and your own. Accepting the home currency hands the conversion to a different party at a worse rate.
Two different rates are available at the same moment
A card transaction can be converted by the card network, which uses a wholesale rate with a modest margin, or by the merchant's payment provider.
When the terminal offers to charge in your home currency, it is proposing the second route. The provider sets the rate and keeps the difference.
Both conversions happen at the same instant using the same market prices, so the gap between them is margin rather than timing.
The margin is embedded, not itemised
The screen typically shows a converted total and sometimes the rate used, but rarely a comparison against the wholesale rate.
Because the cost appears inside the exchange rate rather than as a fee, the transaction can look like a service that removes uncertainty at no charge.
The certainty is real, in that you see the home-currency amount immediately. What it costs is not visible without checking the rate independently.
Declining is straightforward
Choosing the local currency sends the transaction to the card network for conversion, which is the default behaviour when no offer is made.
The amount then appears on the statement converted at the network rate, plus whatever foreign transaction fee the card itself charges.
That card fee still applies either way, so accepting the merchant conversion does not avoid it. The two costs stack rather than substitute.
Cash machines apply the same mechanism
Withdrawals abroad present an identical choice, and the machine operator's rate is subject to the same margin as a shop terminal.
Machines in airports and tourist areas are frequently operated by independent companies rather than banks, and these tend to apply the widest margins.
Bank-operated machines away from arrival halls generally offer better terms, and withdrawing larger amounts less often reduces the effect of fixed fees.
Why the offer keeps appearing
Terminals present the option automatically because the payment provider earns from acceptance, and merchants often receive a share.
Staff are frequently unaware of the difference and will select whichever option the screen highlights, so the choice may be made before the customer sees it.
Asking to be charged in local currency at the outset avoids the situation entirely, and reversing an accepted conversion afterwards is rarely possible.