In the strictest sense, one could say: A web server serves up static HTML pages and nothing else. Tomcat is a Servlet/JSP container, and 'Java application servers' are those which support the full JEE (formerly J2EE) stack. The distinctions between these terms, however, have always been blurry, and continue to become more so over time, and will vary depending on where and with whom your discussion takes place.
To understand this requires a little history lesson. Tomcat started its life as the JServ module for Apache HTTPD (now known as the Apache web server). It was only a servlet container and was incapable of handling web requests on its own.
When combined, HTTPD would handle all web requests, would serve up all the static content on its own and forward any dynamic requests to JServ. Httpd was the web server and JServ was the servlet container. Eventually, JServ was replaced by the Tomcat application server, and a connector was added that allowed Tomcat to operate as a standalone ... more.
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