There are in fact two markets, the primary and secondary market.

The primary market is where stocks are issued, usually with an IPO. At this point, a company issues the securities, and the banks that underwrite the process (commonly known as underwriters) help distribute them. The distribution takes place in the secondary market.

The secondary market is the actual stock market. Here, the stocks are traded between parties independent of the issuing companies. Once the stock has been issued in the secondary market, the company cannot control the trading of the stock. The NYSE, NASDAQ and AMEX are all secondary markets.