Forex trading

Forex stands for Foreign Exchange. Thus, this business deals with foreign currency.
Forex trading is the appropriate term used for it.

Here is the material I found in Answers.com:

Foreign exchange, also written as FX, is :
1. Transaction of international monetary business, as between governments or businesses of different countries.
2. Negotiable bills drawn in one country to be paid in another country.

Forex - FX
The foreign exchange (also known as "forex" or "FX") market is the place where currencies are traded. The overall forex market is the largest, most liquid market in the world with an average traded value that exceeds $1.9 trillion per day and includes all of the currencies in the world.

Investopedia Says: There is no central marketplace for currency exchange, rather, trade is conducted over-the-counter. The forex market is open 24 hours a day, five days a week, with currencies being traded worldwide among the major financial centers of London, New York, Tokyo, Zürich, Frankfurt, Hong Kong, Singapore, Paris and Sydney - spanning most time zones.

The forex is the largest market in the world in terms of the total cash value traded, and any person, firm, or country may participate in this market.