Lightning network = You hold 1 of the 2 private keys that holds the bitcoin in the lightning channel.  You can unilaterally close the channel at any point in time.

Liquid network = in order to withdraw bitcoin from the liquid network, you don't hold any of the private keys.  You are relying on a 11 of 15 multisig to approve your withdrawal, otherwise known as a federation. Up-side is blocks are confirmed every minute, transactions are confidential, and transactions fees are generally cheaper than the base layer.