Even the concept of an exchange rate was different two hundred years ago from what it is today. Today, the interbank rate quoted for a currency is for delivery today, or even this second. Two hundred years ago exchange rates were primarily futures rates. If someone were traveling from the United States to England, or shipping goods between the two countries, they would need to know the exchange rate when the money or goods were transferred. Foreign exchange quotes were provided for sending a letter of credit to that city, not country, in order that the goods could be paid for once that person had arrived in that country, or so money could be transferred from one country to another.
Today, people can keep accounts at a bank in the currency of their choice. Two hundred years ago this would have been pointless. People in London did not keep French Francs, German Marks and US Dollars, though they might have wanted to transfer funds to Paris or New York in order to send money to someone in the other country or to have money awaiting them when they arrived in that country. The situation was further complicated by account (banco, bankgeld, etc.) money, or "ghost" money as Carlo Cipolla called it. Just as today, governments can reduce the value of their currency by "printing" money through open market operations, in the past, governments would debase their currency by reducing the silver and gold content of their coins. The Revolutionary War provides a good example of this. If someone had contracted to purchase a farm for $1000 prior to the war, the inflation of the Revolutionary War would have lowered the cost in specie money to only $1, since after the war, it took one thousand paper dollars to purchase one silver dollar. After the Revolutionary War, farmers actually took pigs to the market, sold the pigs, and used the proceeds to buy their entire farm! This was obviously a great deal for the farmer debtors, but a rotten deal for the creditors. Account money prevented situations like this from happening. Another reason for the existence of account money was that the subsidiary divisions could fluctuate against one another. For example, someone might owe 40 Shillings on account, which was equal to 2 Pounds Sterling, but the value of the 40 silver shillings might fluctuate against the value of the 2 Gold Pounds Sterling. A country might start out using pounds, shillings and pence as their units of account, but the pound would be made of gold, the shilling of silver and the pence of copper. A pound might start out being worth 240 copper pennies, but in a few decades might be worth 480 pennies as the pennies became debased. Now the debtor would have to pay with 1 Gold Sovereign or 480 copper pennies, not 240 pennies. Bank money did not depreciate over time as the value of specie money or paper money changed. It protected creditors against debasement, and lenders against deflation. The agio calculated the difference between the value of bank money and "current" money.
Some countries had no legal tender, or several, and the debt could be paid in pounds or francs, silver or gold. Gold, silver and copper coins changed their values relative to one another over time as the supply and demand for different commodities changed, and as the government changed the commodity content of different coins. Eventually, the commodity value of coins was eliminated altogether.
In many countries, there were not only three different versions of each "money", but different currencies that circulated simultaneously. Small countries or colonies might accept several foreign currencies as legal tender, or use the coins from several different countries. If the Maldive Islands could not afford to create its own currency, it was easier to use someone else's money instead. Even if the Maldive Islands introduced its own currency, its citizens might trust foreign currencies more than their own, even as people in many countries trust the United States Dollar today than their own domestic currency.
Countries like Germany lacked a single currency because different principalities, bishoprics, or other political entities could issue their own money. A government could devalue its currency by reducing the silver or gold content, by declaring old currency worthless, or making it worthless through inflation. Even in countries that might have a single system, monetary chaos could reign. Spain at one point had 139 different coins circulating simultaneously within the country.
Within each country, coins from different nations might circulate freely according to supply and demand. In the United States, the Spanish Real and Half-Real were preferred to the dime and half-dime in the early 1800s. Just as United States Dollars are used as a medium of exchange in countries throughout the world, Spanish Trade Dollars, Maria Teresa Dollars and other coins were just as likely to circulate outside of their country of origin as in the country where they were minted.
Until the Twentieth Century, this was the norm. You might have had a single monetary system for a country, but the values of the media of exchange fluctuated against one another. The result was chaotic. Although the Twentieth Century led to a proliferation of national currencies, it did produce a unification of the currency within each country.