Installed software is the raw name of the software which is collected via inventory. Whereas, normalized software is the user-friendly name defined either manually or by defining the Normalization rules.
Use case: One reason for using normalized software name is to see user friendly name for easy identification. Other usage is to club multiple sub versions to a common name. For example, ‘Firefox 60.1’, ‘Firefox 60.2’ can be normalized to a name ‘Firefox’ for easier understanding. Normalization is also used to normalize different manufacturer names represented such as Microsoft, Microsoft Corp, Microsoft Inc which gets enumerated as part of software inventory to common normalized name say Microsoft Corporation.