A wallet is a product that allows you to store a crypto asset (e.g., cryptocurrencies).
The difference between custodial and non-custodian wallets comes down to who controls the private keys for a wallet, which determines who has access and can manipulate the contents of the wallet.
A non-custodial wallet is a decentralised type of wallet, where the customer owns its private keys. On the contrary, a custodial wallet is a type of digital wallet which keeps a customer’s private key as a part of the provided service and provides other services like backup and security of crypto assets.
To illustrate the difference, Binance utilises a custodial wallet, whereas NuFi utilises a non-custodial wallet.