Many application developers do not focus much on the infrastructure on which their code runs. When it comes to web applications there are common confusions like what is the difference between webserver and applications server or when to go for a EAR vs WAR file deployment etc...
There are many good answers that differentiate between web servers and applications servers like this one. Most of the times the terms Web Server and Application server are used interchangeably. This article explains the working of a typical web server. Typically we get confused with the example of Tomcat Server (an example for a web server) having the capability to run the enterprise applications. So, tomcat is a web server or an application server? Let me tell you how I convinced my self regarding this.
Some time back I was struck with the question What's the difference between JPA and Hibernate on stack overflow. I did answer it, but one of the comment lead me to a more detailed understanding of the JavaEE spec and certified servers. If you can understand this then differentiating between the web server and application server is easy. During my investigations I got this article, which discusses the advantages of both.
A more detailed look in to the meaning JavaEE specification will throw some light in to our discussions. As we know specifications are set of rules. Simply put they contain the interface. Any JavaEE servers which needs to comply to spec needs to have the implementation of these interfaces. You can find the certified JavaEE servers list here. If you are deploying your enterprise applications (means you have JPA, EJB or some technology which is part of Java EE) to the a server which comply to JavaEE then the lib need not contain the API implementation jars. But these are needed if you are using a web server like tomcat for deployment.
For example, if you use JPA in your applications and deploying it to the Jboss AS 7, then you need any additional jars in the lib. But the same application you want to deploy to the tomcat server then you need to have additional jars to lib that implements the JPA spec may be eclipselink or Hibernate. This is what makes JBoss AS 7 an application server and tomcat a web server. Another key difference is that we can not deploy an EAR file to tomcat, it could only handle WAR files.