Custodial means a third party holds your funds; non-custodial means funds settle directly to a wallet you control. Custodial processors can reserve or freeze balances; non-custodial settlement gives you immediate, sole control.
The trade-offs
Custodial services can be convenient and offer chargeback handling, but they hold your money and set the rules. Non-custodial settlement puts you in control and removes freeze/reserve risk, with the responsibility of managing your own wallet.
Part of our guide to non-custodial payments.