Grant Fritchey discusses Azure SQL Database wait stats:
You’ll notice that these results are wildly different from those above. What we’re looking is largely a server versus a database, but not completely. I mean that sys.dm_os_wait_stats is showing the waits for the instance on which my primary Azure SQL Database is currently running. Most of those waits are mine, but because it’s part of the management structure of Azure, sys.dm_os_wait_stats shows some information that’s not applicable, directly, to me. The “server” is not really that. It’s a logical container holding your database. There’s a lot more to it under the covers. To get the waits that are absolutely applicable to me and my databases, I have to go to sys.dm_db_wait_stats.
Azure SQL Database is going to behave a bit differently from on-premise SQL Server, so if you’ve got an Azure SQL Database, pay attention to those differences.