The Creative Cloud includes both desktop applications and services like Typekit and Edge Web Fonts.
The fonts included with the current CS6 desktop applications are detailed here http://www.adobe.com/type/browser/fontinstall/cs6installedfonts.html.
Both Typekit and Edge Web Fonts are web font services, so work for web design.
A paid Individual subscription or paid Seat on a Team subscription includes the Portfolio plan for Typekit. Details here https://typekit.com/plans. A free/trial accoun includes the Trial plan for Typekit.
Edge Web Fonts are a free web font service and are detailed here http://html.adobe.com/edge/webfonts/ and here http://blog.typekit.com/2012/09/24/introducing-adobe-edge-web-fonts/.