In a custodial wallet, you give your money to whatever person or group made that wallet, they handle the difficult parts of running a node for you, and they give you nice and easy "Send" and "Receive" buttons. A node, by the way, is a software program that is designed to regularly communicate with similar programs on a network. They are used a lot in bitcoin and on the lightning network.

In a self-custodial wallet -- sometimes called a non-custodial wallet -- your money (well, your private keys) are directly on your own device. Your device runs a node in the background, usually (if it's a phone) in a kind of "lite mode" where communication is less constant, and it tries to automate some parts of managing a node. But it usually requires some initial setup and occasional maintenance, either via user prompts (e.g. "please pay 50,000 sats to open a new lightning channel") or some dedicated "Manage" interface.

In short, custodial wallets are easier to use but you don't actually "have" your money -- whoever made the wallet does. Self-custodial wallets are harder to use but they give you full control over your money because you, and you alone, have the private keys.