As Bear said, there are many definitions of what an app server is. If an application consists entirely of servlets, JSPs, and their associated classes, then it can be hosted by Tomcat, and that would make Tomcat an app server.
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so you mean there is no difference in an application server and a web server responsibilities.
Generally, application servers, like IBM WebSphere AS, Oracle AS, Sun AS, BEA WebLogic AS, JBOSS AS are officially certified for implementing a particular version of the J2EE specification. Tomcat only implements a very small subset that includes JSP+Servlets mainly so it doesn't really get much of a label as "application server" which provides much more enterprise services.