stock market is a private or public market for the trading of company stock and derivatives of company stock at an agreed price; both of these are securities listed on a stock exchange as well as those only traded privately.
The stocks are listed and traded on stock exchanges which are entities (a corporation or mutual organization) specialized in the business of bringing buyers and sellers of stocks and securities together. The stock market in the United States includes the trading of all securities listed on the NYSE, the NASDAQ, the Amex, as well as on the many regional exchanges, e.g. OTCBB and Pink Sheets. European examples of stock exchanges include the Paris Bourse (now part of Euronext), the London Stock Exchange and the Deutsche Borse.
The expression 'stock market' refers to the system that enables the trading of company stocks (collective shares), other securities, and derivatives. Bonds are still traditionally traded in an informal, over-the-counter market known as the bond market. Commodities are traded in commodities markets, and derivatives are traded in a variety of markets (but, like bonds, mostly 'over-the-counter').
Many years ago, worldwide, buyers and sellers were individual investors, such as wealthy businessmen, with long family histories (and emotional ties) to particular corporations. Over time, markets have become more "institutionalized"; buyers and sellers are largely institutions (e.g., pension funds, insurance companies, mutual funds, hedge funds, investor groups, and banks). The rise of the institutional investor has brought with it some improvements in market operations. Thus, the government was responsible for "fixed" (and exorbitant) fees being markedly reduced for the 'small' investor, but only after the large institutions had managed to break the brokers' solid front on fees (they then went to 'negotiated' fees, but only for large institutions).