A Lightning Wallet allows you to interact with the Lightning Network to send and receive bitcoin. They keep track of your balance and your transaction history.
Lightning Wallets establish channels, calculate routes on the network, manage channel opening and closing, and in some cases, ensure constant uptimes.
There are maily two types of Lightning Wallets, custodial and non-custodial.
Сustodial Lightning Wallets are wallets that use someone else's Lightning Node (most often the company that created the wallet). They manage the creation of channels for you. The biggest advantage of custodial wallets is that they are very user-friendly. The biggest disadvantage is that you do not control your own private keys and are dependent on the wallet company to saveguard your funds. There is always a risk that your money can be stolen.
Non-custodial Lightning Wallets need their own private Lightning Node and manage their own channels. These wallets require more understanding and are less user-friendly than custodial wallet solutions. With a non-custodial wallet, you control your own keys and funds. No trust in an intermediate company is needed.
New hybrid types of wallets are also being developed, whereby you can use someone else's lightning node, yet control your funds and keys yourself. These wallets will then combine the usability of custodial wallets with the safety of non-custodial wallets. These wallets make use of the Neutrino light wallet protocol.