A Lightning wallet is always based on a functioning Bitcoin wallet. Being able to receive and send via Lightning is therefore usually simply an additional feature. Lightning payments are faster and cheaper than normal Bitcoin transactions.
As with Bitcoin wallets, there are custodial and non-custodial wallets. In other words, those wallets where you exchange a simpler user experience for holding your own keys, and those where you retain access to and responsibility for your funds. So think carefully about how many assets you want to park on a custodial wallet.
If you want to know which different Lightning wallets are available, read the support article Which Lightning wallets are there?