J2SE = Java 2 Standard Edition: the normal version of Java which runs on desktop and laptop computers
J2EE = Java 2 Enterprise Edition: an extension to J2SE for server-side Java programming
J2ME = Java 2 Micro Edition: a special version of Java for mobile phones (which is getting obsolete soon, in my opinion, while phones get more and more powerful)
Try Googling for "what is J2EE" etc. for more information.
here is one difference besides the definition
J2EE includes the class required for J2EE development(example jsp,servlet,ejb api's etc.)
To use it you also need J2SE, think of it as an add on module like for J2SE.
you will more clear about this, when try to download the J2EE kit or J2SE kit from sun website
they will clearly mention you the components each will contain.