What Is the Primary Difference in How Slippage Is Calculated on an AMM versus a CLOB?

On a CLOB (Central Limit Order Book), slippage is calculated as the difference between the expected execution price (e.g. the best bid/ask) and the actual executed price, based on consuming the discrete price levels in the order book. On an AMM, slippage is calculated based on the change in the ratio of assets in the liquidity pool, as determined by the pricing formula (e.g.

$x y=k$). The AMM's slippage is a continuous function of the trade size and pool depth.