Compatibility testing, part of softwarefunctional tests, is testing conducted on the application to evaluate the application's compatibility with the computing environment. Computing environment may contain some or all of the below mentioned elements:
Computing capacity of Hardware Platform (IBM 360, HP 9000, etc.)..
Other System Software (Web server, networking/ messaging tool, etc.)
Certification testing falls within the scope of compatibility testing. Product Vendors run the complete suite of testing on the newer computing environment to get their application certified for a specific Operating Systems or Databases.
Server Compatibility Level is specific to servers and it dictates how specific language elements of the database functions in relation to previous versions. In other words, it's the "backwards compatibility" of a server to an earlier versions.
Browser compatibility (Chrome, Firefox, Netscape, Internet Explorer, Safari, etc.) Browser compatibility testing, can be more appropriately referred to as user experience testing. This requires that the web applications are tested on different web browsers, to ensure the following:
Users have the same visual experience irrespective of the browsers through which they view the web application.
In terms of functionality, the application must behave and respond the same way across different browsers.