Sun changed the name a bit. The first release of Java was simply called Java.
Then the platform was updated and was called Java 2, and we got such versions as: Java 2 versions 1.3, 1.4 ... And you got the names of Standard Edition, similar to: J2SE 1.3, 1.4, ...
Enterprise Edition follows the same pattern: Java 2 Enterprise Version 1.2, 1.3 ... Which was released by J2EE 1.3, ...
Because it confused people why Java 2 had version 1.x for a long time they renamed it to later versions: Java Standard Edition 5.0, 6.0, 7.0 or just Java 5 and Java 6 instead of J2SE 1.5 and J2SE 1.6.
Enterprise Edition followed the lead of JEE 5 instead of J2EE 1.5.
The difference is that Java Enterprise Editions <version 5 such as J2EE 1.3 or J2EE 1.4, while Java Enterprise Editions> = 5 will have names such as JEE 5, JEE 6, ...