An order book is the live list of buy and sell orders for an asset, organised by price. A matching engine pairs compatible orders to produce trades.
An automated market maker (AMM) is a type of decentralized exchange that prices trades with a formula over a pool of tokens. It replaces order matching, so anyone can trade against the pool at any time.
A centralized exchange (CEX) is a crypto trading platform run by a single company that holds customer funds and matches buy and sell orders on its own servers. It works much like a traditional brokerage.
A hybrid exchange is a trading platform that combines parts of centralised and decentralised exchanges. It typically matches orders off chain for speed while settling trades or holding funds on chain.
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