What does that mean for you?
In a custodial account, the operator controls the spending keys. You sign into its account and ask it to act. With keys you manage yourself, you are responsible for keeping the recovery information safe.
The same word, wallet, may be used for different arrangements. Ask about control and withdrawal rather than relying on the label alone.
Can you picture an example?
Imagine an account shows a bitcoin balance and a send button. The operator might still hold the keys and decide when withdrawals are available. A button on your screen does not prove direct key control.
What should you remember?
Distinguish a service's account record from a payment on the Bitcoin network. Understand what happens if the account is restricted or the operator fails. This is a comparison of roles, not a recommendation for either arrangement.