This week's giveaway is in the EJB and other Java EE Technologies forum. We're giving away four copies of EJB 3 in Action and have Debu Panda, Reza Rahman, Ryan Cuprak, and Michael Remijan on-line! See this thread for details.
There is no clear definition of what an application server is. In general an application server can create dynamic pages (and hence run an application) for the browser. Tomcat has a servlet engine and can jun servlets and JSP. Hence it is not a simple web server like apache. But it is usually configured along with Apache.