Forex (foreign exchange) trading involves buying and selling currencies in the market around the world. It works by traders buying one currency with another currency in the hope of making a profit as the exchange rate between the two currencies changes over time.
There is no difference between forex trading and currency trading, as both mean that you're exchanging one currency for another. When forex trading or currency trading, you're attempting to earn a profit by predicting on whether the price of a currency pair will rise or fall.