Yes, Avax does run on Ethereum. Ethereum is a decentralized platform that runs smart contracts: applications that run exactly as programmed without any possibility of fraud or third party interference.
NOTE: WARNING: Avax is not built or operated on Ethereum. Although it may appear similar to Ethereum, Avax is its own distinct blockchain platform that runs on Avalanche consensus. It is not compatible with Ethereum and attempting to use it as such could result in serious problems.
Avax is a decentralized platform for buying, selling, and transferring digital assets. Avax uses the Ethereum blockchain to power its smart contracts and transactions.
This means that Avax is a trustless and secure platform, and that users can be sure that their transactions will be processed correctly and securely.