This overview shows that Microsoft has been delivering BI capabilities to help customers model, analyze, and deliver business insights, which can be consumed by business users on mobile devices.
You will see here how Microsoft map component/services on-prem to cloud to deliver hybrid model.
this would help customers analyze high volumes of data, which might already be stored in the cloud, for example in an Azure SQL Data Warehouse, we are now enabling BI semantic data modeling capabilities in the cloud.
Azure Analysis Services, is based on the proven analytics engine in SQL Server 2016 Analysis Services. Customers can access data sources across on-premises and the cloud, model that data, and provide business users with a simplified view of their data to enable interactive self-service BI and data discovery using their preferred data visualization tool.
These three offer share the same processing in-memory engine On-Prem SQL Analysis Services,
Azure Analysis Services and Power BI