Normal bitcoin wallets carry out their transactions and interact with the main network directly, meanwhile Lightning Wallet is a scaling solution, we usually call it layer 2, this method uses lightning channels for transactions. I think i'm still not competent in explaining it, it's better for you to read the article from Blockstream ^[1] so you can understand it more clearly.

[1] https://blog.blockstream.com/education/wallets/what-is-the-difference-between-a-bitcoin-and-a-lightning-wallet/