Barter is often referred to a trade of goods, in the absence of fiat money, say fish for grain, or the other way round. With currency dealers, the transaction involves a trade using different currencies, say between US$ and €. Thus, currency dealers deal with foreign exchange rates between currencies. Put more simply, barter is trade with goods, while exchange is trade between currencies.
The primary difference between barter and currency systems is that the currency system uses an agreed-upon from of paper or coin money as an exchange system rather than directly trading goods and services through bartering.