Oracle server and Oracle application server

Are the terms Oracle server and Oracle application server the same?

No, they are totally different, one is database server and the other application server

Can you please explain the differences and what they each do?

Oracle server, is the database server, that stores the data, and makes it available for user sessions, and for queries.

Oracle applications server, is a tool to transform your SQL statements, to an HTML page, so you can browse the database, through your web browser, it is used also to execute stored procedures,...
most of the time the application server, is used in conjuction, with developer server, and web server.

application servers does a lot of things, executes EJBs, C++ Codes, Perl, PL/SQL (procedures), CORBA. The purpose of this is to use thin clients in PCs, this means that you dont need a very poweful workstation to work. In client-server architecture the workstations needs to be pretty powerful, in this new client-application_server-server architecture rather all the operations that were done in client side in a client-server environment are now done in the application server, of course the codes of programs need to be modified to accomodate this.
The result of this is that the company wont have to upgrade PCs so often rather they upgrade the servers which could be much cheaper if the number of workstations is high