The main difference between Custodial and Self-Custodial (also known as Non-Custodial wallets) is who stores the private backup keys (recovery phrases) for the wallet.
With Custodial wallets, the backup keys are stored with a 3rd party which is referred to as a Custodian. Custodial wallets are typically used by services and exchanges.
Examples of Custodial wallet services:
While with Self-Custodial wallets, the backup keys are stored by the user. Those are generally used by dedicated storage wallets or hardware wallets.
Examples of Self-Custodial wallets: