How Does a Private Mempool Differ from an Off-Chain Settlement Layer?

A private mempool is a private communication channel for submitting a transaction for eventual inclusion on the main chain (Layer-1). The transaction's execution and settlement still occur on-chain.

An off-chain settlement layer (like a Layer-2 rollup or sidechain) executes and settles the transaction entirely outside of the main chain, only posting periodic proofs or state updates back to L1. The private mempool addresses front-running by hiding the order; the off-chain layer addresses it by moving the execution environment.