Azure AppFabric vs. Server AppFabric - today
Windows Azure AppFabric as a brand name doesn't exist anymore; the technologies it used to contain (Service Bus, Access Control Service, and Caching) are now part of the Windows Azure "Client Libraries for .NET". You are correct in that the two AppFabrics had Caching in common, but at this point it's best not to be confused by the AppFabric branding. Think of the technologies involved: Windows Server AppFabric, and Service Bus, Access Control Service, and Caching (within this set of articles: http://msdn.microsoft.com/en-us/library/dd163896.aspx).
Finally, although this article is a little outdated, it will give you some of the historical context: http://social.technet.microsoft.com/wiki/contents/articles/1445.aspx.