Report Server: Report Server defines the nature of installation of SQL Server Reporting Services in your organization. It comes in two modes namely native and share point mode. Native mode is the default and used in 80% of the industry and in SharePoint mode it is integrated with SharePoint. Report Server is made up of two processing engines and a group of extensions responsible for authentication, data processing, rendering and delivery options.
Report ServerDB: Report Server database contains all properties, objects and metadata related to an SSRS unit. It can be accessed using SSMS. Most used tables from this database are Catalog, Execution Log Storage, Subscriptions and Users.
Report Manager: Report Manager is a web based tool built using ASP.NET application to view/access SSRS reports. It’s not available in SharePoint mode.
Commentary: I faced this question in one of my interview and confused the Report Server and Report Manager terminologies. Technically we will be deploying the .rdl file to the Report Manager and what’s the use of Report Server then? After digging into it came to know Report Server is implemented as a Windows Service and will run in the background as SQL Server Reporting Services. With regards to Report Server DB, Had an opportunity to work with it for an audit purpose and it has tons of data related to SSRS and we can generate useful insights from it.For further reading on this topic visit the MSDN site.
Hope it helps someone:)