Or more specifically: Selenium IDE (Firefox plugin) vs Selenium Webdriver (Python and other languages) vs CasperJS (and PhantomJS or SlimerJS)
Selenium allows you, a programmer or non-programmer, to control a web browser and make it do things that you would otherwise do manually. With that ability, you can test your website over and over (and automatically from cron), similate users, or visit any number of web pages and read data (web scraping) on them and save to a file for processing.
If you go to the Selenium website you will...