Centralized

• Deposit your money – either (via bank transfer or credit/debit card) or cryptocurrency => give up control of it.
• Don't own the private key. When user withdraw, user ask the exchange to sign a transaction on their behalves.
• User make transaction: not on chain
• Exchange make a transaction: on chain / allocate balance in its own database => Out of control

Decentralized

• Orders are executed on-chain with smart-contracts and atomicswap
• User do not lost control of their funds