Courtesy: http://msdn.microsoft.com
SQL Reporting Services in SharePoint Integration Mode
When you integrate a report server with an instance of a SharePoint product, items and properties are stored in the SharePoint content databases. This provides a deeper level of integration between the server technologies that effects how content is stored, secured, and accessed.
Storing report items and properties in SharePoint content databases allows you to browse SharePoint libraries for report server content types, secure items using the same permission levels and authentication provider that controls access to other business documents hosted on a SharePoint site, use the collaboration and document management features to check reports in and out for modification, use alerts to find out if an item has changed, and embed or customize the Report Viewer Web part on pages and sites within the application. If you have sufficient permissions within a SharePoint site, you can also generate report models from shared data sources and use Report Builder to create reports.
The report server continues to provide all data processing, rendering, and delivery. It also supports all scheduled report processing for snapshots and report history. The following diagram shows the server components together:

SQL Reporting Services in Native Mode
Reports are being hosted in a separate server as Native Mode and developers are adding the reports URL in to the SharePoint Pages. When we open a report by clicking the link in SharePoint page, SharePoint redirected to the Report Server URL. Thus, report server is running as an isolated server from the SharePoint.