Custodial wallet: someone(normally it’s a centralized exchange) keeps a private key. Non-custodial wallet: You keep your private key.

Custodial wallet

Advantages: convenience and feeling safe because the responsibility is on the CEX that you keep your coins. You can get the benefits that the CEX provided such as saving, staking(with low fee)

Disadvantages: CEX can suspend transactions so sometime you cannot withdraw your coins.

Non-custodial wallet

Advantages: you can do anything with your asset, anytime.

Disadvantages: You take full responsibility for your asset. If you lose your seed phase, you may lose your asset.