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.

Please start reading these guides:

Is not about preferences or favorites... Is about features, functionalities and use cases. Each wallet will have its own use case.

@DarthCoin, did you get that?

At first it is complicated, another initial tells you... But after you understand the concept it is easy, the "custodian wallets" you are not the one who actually holds the funds, and it depends on the provider's channel, which could escape whenever you want, closing the Channels and obviously taking the sats that said channel had... Now on the other hand the "non-custodial wallets" you personally are the custodian, it is up to you to store the keys that give access to the sats and it is up to you to open or close channels to manage your sats... Only depending on the nodes of those wallets to connect the sats between channels, but you place the sats of the channel and you open and close the channel whenever you want... As a newbie that I am I would also say that the one who best solves our problems is Phoenix.... Blitx and Green are doing well but Phoenix is ​​everything very simple. I hope my opinion helps you

If you are on Android, try the best in class Valet, a fork of SBW. Install and open real channel with deezy or blocktank LSP. I heard they keep channels open for long.