Currency options are the same instrument as the FX option: a contract that gives its holder the right, without the obligation, to exchange a set amount of one currency for another at an agreed rate on or before a given date. The two names are interchangeable, and the main entry covers how the contracts are quoted, priced and used. "Currency option" is the more common wording on exchanges and in textbooks, while dealers in the interbank market tend to say "FX option".
One feature sets these contracts apart from options on shares. Every currency option is at once a call option on one currency and a put option on the other. The right to buy euros with dollars is also the right to sell dollars for euros. The standard pricing formula is a version of the Black-Scholes model adapted to allow for two interest rates, one for each currency.
Most currency options trade over the counter between banks and their clients, where amounts and dates can be tailored for FX hedging. Exchanges list standardized contracts as well, including options on currency futures. Quotation is by implied volatility in the dealer market.