This week's book giveaway is in the OO, Patterns, UML and Refactoring forum. We're giving away four copies of Refactoring for Software Design Smells: Managing Technical Debt and have Girish Suryanarayana, Ganesh Samarthyam & Tushar Sharma on-line! See this thread for details.
Webserver gives you the HTTP/HTTPS service, where as an application server [J2EE compliant app server] is supposed to give you all the support your app needs in J2EE [eg: EJB container, messaging support, thread and database pooling, clustering services, to name a few]
However, having said this, this is just a very superficial take on the differences between these two, and there are many if you care to look deeper under the hood. To put this plainly, webserver, could be treated as a sub-set of an app server.