A centralised exchange is a company that maintains an order book. Buyers post bids, sellers post asks, and the venue matches them. When a trade executes, nothing happens on any blockchain: the exchange simply updates two rows in its own database. Coins move on-chain only when a customer deposits or withdraws. Everything in between is an internal ledger entry, which is what makes the trading fast and what makes the customer a creditor.
That last point is the one worth dwelling on. A balance shown in an exchange account is a claim on the exchange, not possession of an asset. If the company is solvent and honest the distinction never surfaces. If it is not, the customer is an unsecured creditor of a company that also chose which assets to list, set the fees, and in several documented cases traded against its own users. The industry's standard phrase — not your keys, not your coins — is a description of this legal reality rather than a slogan.
Proof-of-reserves attestations were introduced to address it and address about half of it. A well-constructed attestation demonstrates that the exchange controls addresses holding at least as much as the sum of customer balances, usually via a Merkle tree a customer can check their own balance against. What it does not show is liabilities that are not customer balances: loans taken against the reserves, obligations to affiliates, or funds borrowed for the day the snapshot was taken. Reserves without audited liabilities is half a balance sheet.
Decentralised exchanges replace the order book with a smart contract. The dominant design is the automated market maker, where liquidity providers deposit two assets into a pool and a formula sets the price from the ratio between them. Trades execute against the pool, providers earn a share of fees, and no company holds anyone's coins — the trade settles on-chain, from the trader's own wallet, in a single transaction.
The risks simply change shape. A pool's contract can contain a bug, and a bug in a contract holding assets is a bug that gets found. Providing liquidity exposes a provider to divergence loss: when the two assets move apart in price, the pool rebalances against the provider, and fees may or may not cover the difference. Prices on a small pool can be moved by a large trade, and bots reorder transactions inside a block to extract value from predictable ones. There is also nobody to appeal to. A transaction sent to the wrong contract is gone.
Two practical points apply to both kinds. Deep books and deep pools matter more than headline fees: the spread and the slippage on a real order usually cost more than the commission. And withdrawal is the only test of custody that means anything — an account balance is a promise until it has been moved off the venue and confirmed on-chain.