Put simply, Amazon Managed Blockchain is a "traditional" blockchain whereas Amazon Quantum Ledger Database is something totally different. Amazon Managed Blockchain is a fully managed service for creating and managing blockchain networks using open source frameworks. Currently, the Hyperledger Fabric open source framework is supported. Blockchain allows you to build applications where multiple parties can securely and transparently run transactions and share data without the need for a trusted, central authority whereas, Amazon Quantum Ledger Database (Amazon QLDB) is a fully managed ledger database owned by a central trusted authority that provides a transparent, immutable, and cryptographically verifiable transaction log of all of your application changes. Amazon QLDB tracks each and every application data change and maintains a complete and verifiable history of changes over time. This one is quite different. The story is the customers were looking at Blockchain as a way of providing verifiable transactions. Then Amazon realised that this goal does not require a full distributed nature of a blockchain. Instead, it just needs a central database with verifiable transactions.
