Corporate just indicates a business's software, some software such as Microsoft Windows and Norton Antivirus, provide a 'corporate edition' to their usual software. The differences is that the program may not require a serial key (in Microsoft windows corporate edition), others such as Norton Antivirus tend to be more cut down and versatile with special features such as availaiblity to run software in the background without user noticing, and automatically updating, and even configuring the software via a server.
Other corporate software has special features (additionally) on its normal software that supports running on servers, or features that will allow multiple users to use software ... A basic feature would be the 'profiles' you are allowed in some programs, thats a very basic corporate software feature, but thats only for you to get a basic idea of what the difference is, i wouldn't go in armed with that, use hte examples I have, sometimes you can only explain something with an example.
Non-corporate software is just software you're using now, like internet explorer, although a business can use it, its not made specifically for a business...
i hope that was clear, gl