J2EE is a specification to define how application servers should work. These servers attempt to be 'J2EE complient'. When you download J2EE from Sun, you also get the 'reference implementation', which is like a sample of many J2EE components in action, but is not meant to be used for production systems.
Tomcat is a free application server that implements the Servlet Engine subset of the J2EE functionality. Tomcat is a step closer what you need in a production system, but it is a matter of debate as to whether
you should or not.
Hence what you get with J2EE is not enough. Tomcat is better, but some commercial products are better again.
Dave