This is something so basic, and i implicetely know it but i always forget to explain it, so this is to remember that.
Java SE = Standard Edition. This is the core Java programming platform. It contains all of the libraries and APIs that any Java programmer should learn (java.lang, java.io, java.math, java.net, java.util, etc...).
Java EE = Enterprise Edition. From Wikipedia:
The Java platform (Enterprise Edition) differs from the Java Standard Edition Platform (Java SE) in that it adds libraries which provide functionality to deploy fault-tolerant, distributed, multi-tier Java software, based largely on modular components running on an application server.
In other words, if your application demands a very large scale, distributed system, then you should consider using Java EE. Built on top of Java SE, it provides libraries for database access (JDBC, JPA), remote method invocation (RMI), messaging (JMS), web services, XML processing, and defines standard APIs for Enterprise JavaBeans, servlets, portlets, Java Server Pages, etc...