There are two main types of retail FX brokers offering the opportunity for speculative currency trading: brokers and dealers or market makers. Brokers serve as an agent of the customer in the broader FX market, by seeking the best price in the market for a retail order and dealing on behalf of the retail customer. They charge a commission or "mark-up" in addition to the price obtained in the market. Dealers or market makers, by contrast, typically act as principals in the transaction versus the retail customer, and quote a price they are willing to deal at.
Non-bank foreign exchange companies offer currency exchange and international payments to private individuals and companies. These are also known as "foreign exchange brokers" but are distinct in that they do not offer speculative trading but rather currency exchange with payments (i.e., there is usually a physical delivery of currency to a bank account).
Some investment management firms also have more speculative specialist currency overlay operations, which manage clients' currency exposures with the aim of generating profits as well as limiting risk. While the number of this type of specialist firms is quite small, many have a large value of assets under management and can, therefore, generate large trades.
"Forex" stands for foreign exchange and refers to the buying or selling of one currency in exchange for another. It's the most heavily traded market in the world because people, businesses, and countries all participate in it, and it's an easy market to get into without much capital. When you go on a trip and convert your U.S. dollars for euros, you're participating in the global foreign exchange market.
Forex banks, ECNs, and prime brokers offer NDF contracts, which are derivatives that have no real deliver-ability. NDFs are popular for currencies with restrictions such as the Argentinian peso. In fact, a forex hedger can only hedge such risks with NDFs, as currencies such as the Argentinian peso cannot be traded on open markets like major currencies.
More specifically, the spot market is where currencies are bought and sold according to the current price. That price, determined by supply and demand, is a reflection of many things, including current interest rates, economic performance, sentiment towards ongoing political situations (both locally and internationally), as well as the perception of the future performance of one currency against another. When a deal is finalized, this is known as a "spot deal." It is a bilateral transaction by which one party delivers an agreed-upon currency amount to the counter party and receives a specified amount of another currency at the agreed-upon exchange rate value. After a position is closed, the settlement is in cash. Although the spot market is commonly known as one that deals with transactions in the present (rather than the future), these trades actually take two days for settlement.