What's the difference between Adsense and Adwords?

Google Adwords is the proprietary advertising program that produces those prime text only ads on the right hand side of its search engine results page.
Adsense is Google's syndication service for its AdWords ads. Adsense publishers show Adwords ads on their site, and are compensated for each ad that is clicked.
Indeed, Adwords is the advertising program through which people buy text ads from Google. Those ads can run on Google's site, on their partners' sites like another search engine for example. Advertisers PAY to run Adwords ads. They have the option of whether or not they want their ads to be run on the content network (publishers/webmasters websites) or not.
The Adsense program refers to the program that publishers sign up for to run those Google ads on their site. Adsense is the contextual ad program running on people's pages. Publishers do NOT pay; Google pays money to THEM for each click originating from their pages.