Web server: serves content to the web using http protocol.

Application server: hosts and exposes business logic and processes.

Web Server Programming Environment

Apache PHP, CGI

IIS (Internet Information Server) ASP (.NET)

Tomcat Servlet

Jetty Servlet

Application Server Programming Environment

WAS (IBM's WebSphere Application Server) EJB

WebLogic Application Server (Oracle's) EJB

JBoss AS EJB

MTS COM+

On a first hand, a web server serves web content (HTML and static content) over the HTTP protocol. On the other hand, an application server is a container upon which you can build and expose business logic and processes to client applications through various protocols including HTTP in a n-tier architecture.

An application server thus offers much more services than an web server which typically include:

A (proprietary or not) API

Object life cycle management,

State management (session),

Resource management (e.g. connection pools to database),

Load balancing, fail over...