The primary difference between widgets and badges are the uses. Badges are mostly used by someone curious in seeing how much traffic their site gets via link from other site or even search engines. This gauges them against other site in the same realm of interest and governs what sites they should perhaps purchase link space. Badges can keep track of visitor and show where the visitor came from to get to said site. This is a great tool for site for something like health food. If their site is getting more traffic from BurgerKing.com or NowandLater.com than GNC.com or WebMD.com, they are more likely to withdraw from the healthier site and go to where their audience is.
Widgets are downloadable desktop applications that help someone do an assortment of things. From scrolling through one’s picture album to finding out stock information, there is a widget for almost anything you can think of: games, news, gossip, twitter, etc.
The best way I think a company could use a widget would be a site like CDNow.com. There is a growing number of people that hear a song or an artist, and automatically open up iTunes, go to the iTunes store and search that artist. The widget would be a nifty was in curbing a couple of seconds off of your search, especially if there is more than one artist one is curious about. The widget could be right on the desktop and as the web viewer scrolls through pages, she can quickly type the artist’s name and have that pop up in a new window instead of having to switch back and forth between Internet browser and iTunes.