No, "being more robust" is the wrong way to think about it. J2EE is the web-application framework for Java. If you want to program servlets, JSP's, etc, then you need J2EE. J2SE is the core functionality, which is not included with J2EE.
Here's Sun's page on certifications.
SCJP is Sun Certified Java Programmer, and I think the next one is SCJD - Developer. These are for J2SE - the core Java system. This is knowledge that can apply across all Java technologies.
It used to be (I think) that Sun used the same terminology for J2EE certification, but they have since changed it. Basically you'll be tested on J2EE specifics, as opposed to anything in the J2SE exam.