FOREX is the simultaneous buying of one currency and selling of another. Currencies are Traded in pairs, for example Euro/US Dollar (EUR/USD) or US Dollar/Rupees (USD/INR). So basically, Forex is trading of currencies.

Stock market or as also known as equity market is a place where shares of companies are traded either through exchanges or over-the-counter mechanism. Share is a slice of ownership in the company and traded in stock market at mutually agreed upon price based on the company's future performance.