I cannot speak to whether your software installations are in compliance or not.
The Software Classification report is based on the Software Classifications panel, which allows you to assign discovered software components to software products, or to exclude, or suppress them. So, the Software Classification report is the best representation of how software products are actually deployed in your environment.
The primary difference in the Software Installations report is that it counts multiple installed instances of a software component as a single installation. As a trivial example, 5 installations of Notepad++ on one machine will count as 1 installation of Notepad++. The Software Classifications report