capybara-webkit and PhantomJS both use Webkit under the hood to render web pages headlessly, i.e., without the need for a browser. They're different tools, however:
- capybara-webkit serves as an adapter for Capybara, a Ruby gem that lets you write and perform high-level UI testing for a Rails or Rack app.
- PhantomJS is a lower level tool that simply lets you run scripts against a web page. It can also be used to write UI tests as well (see Casper, for instance, or any of the other testing tools that build upon PhantomJS).