In an exchange wallet the private key of your wallet is controlled by the exchange and in a personal wallet the private key is in your control.
It’s generally a good idea to store your Cryptocurrency in a wallet where you control the private keys, rather than an exchange where they control the private keys and can be subject to closure, hacks and loss. It’s important to understand an “exchange” is a third party service and a free online open source wallet is a personal storage device.
But different wallets offer different levels of protection. And different exchanges offer different levels of protection. Although exchanges want you to believe that so you keep your crypto with them, but you need to understand keeping crypto on an exchange is not keeping in your custody. On the other hand wallets like Mycelium, Jaxx, Electrum, Ledger Nano S, Trezor, and paper wallets: these are all personal wallets in which you own, hold, and possess your crypto private keys.