Liquidity is an important concept in the world of trading and refers to the ability to buy or sell an asset without affecting its price significantly. In the context of order books and automated market makers (AMMs), there are some key differences in how liquidity is provided and how it affects the trading process.

Order books are a type of trading platform where buyers and sellers submit orders to buy or sell an asset at a certain price. The orders are listed in a book, with the highest bid prices and lowest ask prices displayed. The liquidity of an order book is determined by the number of buyers and sellers participating in the market and the total volume of orders at different price levels. In order to execute a trade on an order book, a trader must match their order with a counterparty that is willing to take the opposite side of the trade.

On the other hand, AMMs are a type of decentralized exchange that uses a mathematical formula to determine the price of an asset based on the ratio of its supply and demand. AMMs are designed to be more resilient to market volatility and fluctuations in liquidity, as they do not rely on order books or counterparty matching. Instead, traders can buy or sell an asset directly from the AMM pool by depositing their assets into the pool in exchange for a proportional amount of a liquidity pool token.

The key differences in liquidity between order books and AMMs are:

1. Liquidity in order books is more concentrated at certain price levels, while AMMs provide liquidity across the entire price range. In order books, the most liquid price levels will have a larger number of orders, while less liquid price levels will have fewer orders. In AMMs, the liquidity is spread evenly across the entire price range, making it easier to trade at any price level.
2. Liquidity on order books is provided by individual buyers and sellers, while liquidity in AMMs is provided by the liquidity pool. In order books, traders must wait for a counterparty to take the other side of their trade, which can result in longer execution times and potentially higher trading fees. In AMMs, traders can buy or sell assets directly from the liquidity pool, which can result in faster execution times and lower trading fees.
3. Liquidity in order books is more sensitive to market conditions and changes in trading volume, while AMMs are designed to be more stable and less affected by market volatility. In order books, changes in market conditions or trading volume can quickly impact the liquidity at different price levels, leading to wider bid-ask spreads and higher slippage. In AMMs, the liquidity is determined by the pool size and the mathematical formula used to calculate the price, which can provide a more stable trading environment.