With a wallet, YOU own the keys and have full control. On an exchange, lots of things can happen. Mt. Gox is the most prevalent example...
https://www.google.com/amp/s/www.wired.com/2014/03/bitcoin-exchange/amp
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Wasn't decentralized. Your currencies are in your hands (just like a LOCAL wallet) like on Bitshares. Unless I am somehow mistaken.