Whoever knows the can move cryptos – nobody else. If you leave them on the exchange, the exchange keeps the key for you. In your own you hold it yourself. Both have their own dangers: with the exchange you trust a company, with your own wallet you trust yourself and your care.
On the exchange
Convenient: buying, selling and withdrawing are quick. How well your balance is protected depends on the provider: in the EU, providers licensed under MiCA must keep customer assets separate from their own. Outside EU oversight, your balance is often just a claim. A deposit protection scheme like a bank account’s usually does not exist either way, and after a bankruptcy or a hack it can take long before you have access again.
In your own wallet
You hold the key yourself, usually secured by a seed phrase of 12 or 24 words. Whoever knows these words has access; whoever loses them and the device as well will never get to the coins again. Transfers cannot be reversed – one mistake in the address can cost everything.
Typical traps
Nobody reputable asks for your seed phrase: no support, no exchange, no wallet provider. Fake apps and websites often look confusingly like the original. That is why many people check new addresses with a small test amount before sending larger sums.