What is difference between Oracle Apps and Oracle Application Server?
Oracle Applications means software that helps you runs your enterprise businesses such as Accounting, Humans Resource, or Financials. But the Oracle Applications Server is the technology that, mostly installs on the server, integrates others software to work together. It can be called Middleware. 

The first example is like Peoplesoft or SAP ERP. The latter is like Apache HTTP Server, Tomcat, Glassfish.