The term for profiting from price differences for the same currency across markets is arbitrage.
In foreign-exchange arbitrage, a trader buys a currency where its price is lower and sells it where the price is higher. The intended profit comes from the discrepancy between markets, rather than from predicting whether a currency will rise or fall. In a textbook example, transactions are made simultaneously or nearly simultaneously to reduce exposure to changing prices.
Arbitrage helps pull prices toward one another. If a currency were persistently cheaper in one market, traders would buy there and sell in the expensive market, increasing demand in the first market and supply in the second. Transaction fees, bid-ask spreads, settlement delays, capital controls, and execution risk can eliminate the apparent gain.
Arbitrage is often confused with hedging. Hedging reduces exposure to an unwanted price movement, while arbitrage exploits a pricing inconsistency. Triangular arbitrage is a related foreign-exchange strategy involving three currencies when their quoted exchange rates do not line up.