I am really disappointed with the web's definitions of these terms, maybe my next stop will be with revising some of those Wikipedia entries. Here are my definitions, let me know what you think.
Web-based: working inside your internet browser instead of on your computer.
Webware: (web + software coined from the site webware.com) are web-based applications that run on the internet inside your internet browser vs software which is installed on your computer and runs on your computer.
WebApps: (web + applications) is another name for webware
See Web 2.0 Directories & Ranking for a list of WebApps & Webware
Widget: a 3rd party webapp tool embedded into a web page. Example: A calculator in your iGoogle or My Yahoo start page)
Webdesk: (I made up this word, this is a project I am working on see www.netvibes.com/webdesk) this is an online suite or collection of tools organized together to create a virtual web-based desktop of webapps and webware.
Example: Microsoft Word is software that is installed on your computer and is computer-based vs Google Docs or Zoho Writer which are web-based word processors that are run inside your internet browser an online instead of on your computer.
Benefits: I have 3 computers. The mac I am issued at work, my Desktop PC in my home office, and my old laptop for surfing the web while watching TV. Instead of me saving my lesson plans on a jump drive and swapping them around from one computer to the next or sendig emails with attachments back and forth to myself, I use Google Docs - a free web-based word process. This webware allows me to work at one WebApps like my Google Docs have made my life much easier and productive.