People seem to assume that currency is converted at exactly the rate that you see posted online. When you google "20 USD in EUR" and it says "14.0964195 euros" they think that means that they can walk into a bank, hand them 20 dollars, and get 14.0964195 euros in return.
The best way to learn about exchange rates is to try and do the exchange yourself. If you're afraid of being ripped off, you're quite welcome to purchase a money order in USD. You knew you could do that, right?
Banks can set the exchange rate to whatever they want. The number you see online is ideal and approximated by a computer model. Banks will either charge a fee for conversion or give you a less than ideal exchange rate, frequently both.
Depending on where you exchange your money, you're probably actually saving money by paying in euros instead of dollars.
EDIT: Also, my response is not to you Pandan, you edited your post while I was typing.