Thank you for posting on the Microsoft Q&A forum and bringing your observation about Azure SQL Database role equivalencies to our attention. We appreciate your diligence and do see your concern about the dbmanager and loginmanager roles and their on-premises SQL Server equivalents.
To explain the equivalencies, the loginmanager role of Azure SQL Database provides the right to create and drop logins in the Azure SQL Database logical server. This maps directly to the loginadmin server role function in on-premises SQL Server, which also controls the creation and deletion of logins. In the same vein, the Azure SQL Database dbmanager role grants users the ability to create and drop databases within the logical server, akin to the dbcreator server role in on-premises SQL Server, which manages database creation and dropping. These equivalencies stem from the underlying duties of each role, concentrating on the administration of server-level logins and databases.
We value your feedback and aim for accuracy. For role equivalency, please see the Microsoft Learn documentation: Database-level roles, Server-level roles
If you have found the answer provided to be helpful, please click on the "Accept answer/Upvote" button so that it is useful for other members in the Microsoft Q&A community.