This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori 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.