J2SE is the core java product, plus APIs for desktop GUI development, and utilities for file operations and network communications. J2EE builds on top of that with tools and APIs for doing server-side enterprise development and deployment. They include things like EJB, servlets, JSP, and related technologies.
to add to what Rob said, the j2ee edition is like an add on to the standard edition. so to work with j2ee you install the j2ee files and etc over and above the standard edition (j2se). I learnt the hard way though