There is Java SE (Standard Edition), which is the standard Java for desktop computers. There is nothing that is officially called "core Java", but when people talk about is, they most likely mean "Java SE".
There is Java ME (Micro Edition), which is Java for small devices such as mobile phones.
There is Java EE (Enterprise Edition), which is a set of APIs on top of Java SE for enterprise applications (mainly software running on servers).
The "Core" part of the Java language has been used as "Core Java" which obviously means the same "Java" or "Java SE", that serves as a base for other editions of Java like "Java EE", "Java ME" as well. [ December 23, 2007: Message edited by: Raghavan Muthu ]