The "two way peg" metaphor is from the original sidechain discussion.

a sidechain is a blockchain where new tokens are created only when on the parent blockchain tokens get locked.

These tokens locked on the base layer can then only be spend, if the second layer tokens have been destroyed.

To some extend this is a money warehouse with transferable notes of deposit.

However the crucial idea originally was that this pay out mechanism is a smart contract, enforced by all Bitcoin nodes and not reliant on a set of trusted entities. This turns out to be not trivial at all, Liquid uses 11-of-15 trusted multisig signers, and even bitVM isn't perfectly trustless, but it's the latest massive improvement to the concept.