Entertainment software includes things like movie players and video games. This software is primarily designed for entertaining the user but it can be expanded to things such as education.
Communication Applications are designed to facilitate the exchange of data between individuals or entities. Programs such as Skype, Google Voice, Email, SharePoint, and many others programs allow this.
Security software includes programs such as antivirus and antispyware applications. It also includes firewalls and many types of encryption and privacy software.
Data safety software is primarily concerned with backing up and preserving the integrity of your information. It attempts to ensure the existence of your data through potential disasters.
Office software applications are designed to help you create documents and forms for consumption in an office environment. It includes software like the Microsoft Office suite, Open Office, Libre Office, and Wordperfect.
Production software applications are designed to help the user create content for other users. Things such as Photoshop, Paint.net, and Premiere, would all be included in this category.
Web Apps are applications that reside on web pages. Shortcuts to these applications might simply be a link to the webpage itself. These applications store data on remote servers and are accessible without installing any software. Things like Pandora, Google Apps, and Photobucket would be considered web applications.
Utilities are programs that perform tasks that would either be tedious or impossible for a human to perform. Transforming data into different types for storage, writing data to other disks, checking data for errors and more would be considered a utility application.