The price of an asset pair on a Centralized Order Book is determined by individual market makers creating buy and sell orders while other participants decide if they want to trade at those given prices.
On the other hand, Automated Market Makers use a mathematical formula to define the price depending on each asset’s balance deposited on the liquidity pool.
For example, Uniswap trading pools only allow two assets, and the price of the pair is determined by the formula x*y=k, as you can see on the diagram below:
What does this mean?
The consequence is that since prices are discovered in a different way on each model, this creates many arbitrage opportunities between CLOB x AMM or even between two different AMMs (Raydium <> Orca)
It is interesting to notice that the only way for the price to move on an AMM is when a swap happens, therefore, arbitrageurs become the main force in helping the AMM keep the price close to all the other markets.
Note: some AMM protocols might allow users to add liquidity on only one side of the pool, and this might also change the pair price.