What is the difference between
upgrade in the context of application software?
Depends entirely on the installation technology, company developing the software and the whim of the person using the terms. Generally though, updates stay within a product version (for example, hotfixes), while if you want to move to a later version, you would upgrade.
So you might install an update (hotfix) for Office 2007, or you might upgrade to Office 2010.
This page gives the definition according to Windows Installer: http://msdn.microsoft.com/en-us/library/aa370579(v=VS.85).aspx
Consider thinking about it this way:
An update is taking something you have and tweaking it a bit, usually to fix something that someone found broken. Quite often the vendor feels obligated to give this for free, since it's what you should have gotten, how it was advertised, or secures something better. Occasionally little improvements and optimizations are delivered as well.
An upgrade is getting the next best thing, which usually is new behavior, features, or compatability. The new software will have noticable functional improvements or additions.
Update - This is simply adding the new modified files in a small scale, but will have the originality with new additions to it.
Ex: updating the Virus Definition in your Antivirus
Upgrade - This is promoting from one level to another level, sometimes the out put product can be a totally changed version of the original which was existing earlier
Ex: Upgrading windows 98 to Windows XP