Basically, Azure SQL databases are classified into three categories:
SQL DatabaseAn Azure SQL Database is a relational database-as-a-service (DBaaS). Here the user doesn't need to take care of the underlying platform or anything. This should be monitoring by using an
Azure SQL database agent, this includes
Azure SQL Elastic Pool monitoring.
SQL Managed InstancesAn Azure SQL Managed Instance falls into the industry category of Platform-as-a-Service (PaaS) and is best for most migrations to the cloud. This should be monitored by using a
SQL Server agent .
SQL Virtual MachinesA SQL Server on Azure VM falls into the industry category Infrastructure-as-a-Service (IaaS) and allows you to run SQL Server inside a fully managed virtual machine (VM) in Azure. This should be monitored by using a
SQL Server agent .