The ways in which stock exchange operates can be separated out into two broad categories of mechanism by which transactions are entered into.

Quote driven and order driven exchanges. Hybrids of these two approaches are also possible. A quote driven exchange operates by having market makers whose job is to quote prices both a bid and an offer price, a price they're willing to buy, and that they're willing to sell at. If you are registered as a market maker for a particular stock, you must maintain a price quote for a minimum number of shares that is specified by the exchange. And the prices that you are quoting are not indicative prices, but rather if you are quoting a price and a counterparty wishes to trade with you at those prices, then the market maker is obligated to trade at their quoted price. Market makers profit as a result of the spread between two prices, the bid and the offer, or the bid and the ask prices that they are quoting. One major exchange that operates purely on a quote driven basis is the NASDAQ. Order driven exchanges on the other hand, operate based on orders placed by market participants. There is no need for any market makers to be involved. The job of the exchange is purely to match buy orders and sell orders for which an agreeable price can be found. The vast majority of order driven exchanges operate on an electronic basis so the systems behind this exchange are just looking for orders placed to buy securities and orders placed to sell securities and matching up those trades, following predefined rules wherever possible. If a trade has been placed to the exchange and cannot be matched, it will be added to a log of unmatched trades that is referred to as the order book. And at the end of any trading day, any unmatched trades will then be deleted. The order book is visible to all members of the exchange so other members of the exchange can see what orders have been placed but not matched by other members of the exchange.

The New York Stock Exchange, the London Stock Exchange and the Tokyo Stock Exchange all operate primarily on an order driven basis.

Some of the major stock exchanges globally are presented in this table. It's possible to see that the New York Stock Exchange is far and away the largest stock exchange by size of companies who are listed through this exchange. The NASDAQ comes second and is primarily tech focused. Both of these two exchanges are based in the US. Then moving down the list, we move to the London Stock Exchange in the UK. Tokyo Stock Exchange based in Japan. Shanghai Stock Stock Exchange based in China. Hong Kong Stock Exchange based in Hong Kong, Euronext which is a suite of exchanges across Belgium, France, the Netherlands, Portugal, and the UK. And then the Deutsche Borse, the German Stock Exchange.