Ooh that's a good one. It includes a detour into some really weird forex stuff. If you're used to it it's not that weird but as a American, with US credit card, and a US bank account who then banks exclusively in USD, I found it complicated and fascinating.

Basically, other countries can bank in USD sometimes, so there's a weird corner case that you can send USD to a merchant but can land in their account as $converted_currency or USD that isn't so corner. I'll let patio11 cover this (if/when he gets to it) as there are details I no longer have access to and thus can't do the subject justice.

As an aside, if you are using no forex fee US credit card, and a foreign merchant asks if you want to pay with USD or the local currency, always choose local currency.

If you choose USD, then the merchant gets to choose whatever exchange rate they want to convert at, and will be far from the spot price (hence some merchants go out of their way to ask you if you want to pay with USD). If you choose the local currency, then your American bank will give you an exchange rate extremely close to the spot rate and the transaction ends up being much cheaper for you.

Even if you have a card that charges an exchange fee, they likely charge a fee for USD denominated foreign transactions too, although it may be slightly less, and the more favorable exchange rate from your bank may cover the fee.

It does not directly answer your question, but many (most?) merchant agreements in EU have significantly higher fees for accepting non-EU cards. E.g. Stripe takes 1.4% vs 2.9% for EU vs non-EU (card-present EMV transactions are typically much lower cost, but that still shows the idea).