What is the technical difference between BTC and LN wallets? Are they generated via a diferrent algorithm or format?
A Bitcoin wallet mainly maintains your private keys and keeps track of the transactions associated to the corresponding public keys or the addresses. The Bitcoin wallet will also help you broadcast your signed transactions.
A lightning wallet does all the same but additionally it follows the lightning network protocol meaning it helps you set up Revocable sequence maturity contracts which are used to construct a payment channel. They are created by a sequence of signed but not broadcasted transactions and revocation keys. The hashed time lock contracts wish are used for routing are maintained in a similar way. All of this is the so called channel state and stored privately in a database of your computer. This state is needed in addition to your private keys to access your funds.