How does a custodial wallet differ from a non-custodial wallet?

TL;DR: In the Bitcoin world, the distinction between custodial and non-custodial wallets revolves around private key access. Non-custodial wallets grant users access to their private keys, meaning they have full ownership and responsibility for their bitcoin. Custodial wallets, on the other hand, hold the private keys for you, providing only a bitcoin-based IOU. While this means the custodian assumes the duty of safeguarding the bitcoin, it introduces third-party risks. Notably, large custodial holdings can become targets for bad actors like hackers or authoritarian regimes. Remember: not your keys, not your coins!

Technically, the difference between custodial and non-custodial hinges on the ownership of the private key that controls the contained bitcoin. Only non-custodial wallets give you access to the private key, while custodial solutions withhold this key from you. So, with a custodial wallet, you do not really own your bitcoin but instead a bitcoin-denominated IOU from the custodian.

Operationally, the difference hinges on the responsibility. With a non-custodial wallet, you are solely responsible for what happens to your bitcoin. Nobody can take them from you, but you might lose them through mishandling, accident, theft, or other mishaps. With a custodial wallet, since you do not own the Bitcoin but an IOU, the custodian, which is usually a business or service provider, takes responsibility for holding and keeping your bitcoin safe. Still, you can usually call on the judicial system in case of unjustified loss. However, this adds third-party risks, and whether or not the custodian will be able to make you whole in case of loss of your funds is another question.

Keep in mind that a custodian for a large sum of bitcoin quickly becomes an attractive honeypot for hackers and other attackers, even national governments. We would advise you to learn enough about Bitcoin, so that you are able to secure them yourself—not your keys, not your coins!