A decentralized exchange (DEX) has some combination of decentralized properties. At the moment this most likely means some mix of 1) on-blockchain trade clearing, 2) ability for users to retain control of their funds, and 3) hosting an orderbook in some decentralized manner. They may run on a decentralized exchange protocol or directly on smart contract protocols. A decentralized exchange protocol defines some combination of: a common trade order format, a way to reward those who spread orders, and a way to complete a trade when a match is found.   Benefits of DEXs:
Benefits of DEX protocols:
Challenges for DEXs: