Difference between an application server and a servlet container?
A servlet-container supports only the servlet API (including JSP, JSTL).
An application server supports the whole JavaEE - EJB, JMS, CDI, JTA, the servlet API (including JSP, JSTL), etc.
It is possible to run most of the JavaEE technologies on a servlet-container, but you have to install a standalone implementation of the particular technology.
Basically an application server in Java EE context is a software installed on a server and that implements one Java EE specification (Java EE 7 for example). That means such software (application server) must be able to run Java EE application.
Java EE defines 4 domains, the so called containers:
- Applet container,
- Application client container,
- Web container, and
- EJB container.
Two containers are part of the application server (EJB and Web container) and two others are part of the client-computer.
JBoss and Weblogic are application servers, Tomcat and Jetty are web container. That's why JBoss and Weblogic can deal with more technologies than a Web container. Application server can manage EJB.
Servlet container is not the appropriate expression to qualified Tomcat and Jetty because it is more restrictive. Tomcat can also execute JSP and JSF, not only Servlets.
Broadly speaking, a servlet container restricts itself more or less to the implementation of the J2EE Servlet specification. Also, it's focus is on the runtime environment and not so much on providing additional tools.
In contrast, a full fledged application server implements the whole J2EE stack; plus it comes with all the enterprisey tools and integration possibilities. An application server usually has advanced administration interfaces, it supports clustering and other features used mostly in high-end systems development.
For a beginner, it's probably better to stay with a simple servlet container, since the learning curve there is much less steep.
Edit
@Apache Fan: It depends on the specifics of your situation like existing systems and future plans among other things. I don't think a generic flowchart approach is applicable here.
Platform selection is usually done by weighing specific requirements against first-hand knowledge of systems under consideration.
However the question gives no clues as to what the evaluation criteria are. Should it be open source? Is around-the-clock vendor support necessary? What kind of an enterprise environment should the system integrate with? Are licencing fees an issue? Any must-have technologies or tools? Etc.
Without knowing the above it's pretty much shooting in the dark.