What is the difference between an application server and a Web server?

Web server is exclusively for handling HTTP requests. Application server provide logic to application programs which can be through any number of protocols.
The Web server
1. Handles the HTTP protocol.
2. The Web server provides functionality of providing an environment in which the server-side program receive the request, the server-side program can execute and pass back the generated responses.
The Application Server
1 . Handles many protocols including HTTP.
2. Provides business logic to the client applications through various protocols.
3. Application server clients include GUI application running on  a computer or a web server itself.
Some java application servers are Apache Geronimo (Apache Software Foundation), Glassfish (Oracle Corporation), IBM Websphere, JBoss (Red Hat),
WebLogic (Oracle), WebObject (Apple Inc.)