Liquid uses a separate blockchain and bitcoin is locked when it is swapped into a liquid token which uses a two way peg to maintaib parity. Transactions take place using liquid's...'alt'...coin environment. When you cash out to on chain, the liquid network unlocks the coin to the address you specify, doing away with the token. The whole network is managed by a trusted Federation with a high degree of centralization. It does also work with things other than Bitcoin.

Lightning involves channels. Btc is locked in a channel with a ywo of two multisig wallet. The nodes on this channel have channels with other nodes. They transact across these interconmected channels. When the channel is closed, they net out the total transactions and do a single on chain transaction, instead of one for each transaction done on the lightning network.