Azure SQL Database is a Plataform as a Service (PaaS) offering, is a managed service were Azure takes care of the hardware, updates to the operating system, updates to Azure SQL database, and many other administrative tasks including automated backups and autmatic tuning. With virtual machines you are taking care of the updates to the operating, system, updates to the database engine, indexing strategy, bbackups, and everything is do it your self. Virtual machines are associated with Infrastructure as a Service (IaaS) and very distant of what is considered PaaS.
With Azure SQL Database, Microsoft is taking care of the hardware, virtual machines and operating system used to host the database. You cannot interact with Azure to decide the virtual machines or hardware where Azure SQL is created. You can only do that with SQL Server instanes but not with Azure SQL database.