BTW, I think the article is a bit confusing regarding the versioning of Java. This is not a surprise, since Java versioning itself is extremely confusing!
Usually, it is best to use the "internal" numbering which is what the JVM itself reports. A quick overview (J2SE only - adding J2EE to the equation makes things incredibly complicated!) including some comments on usage:
1.0.2 - first usable Java - this is what Acorn's Java originally implemented ("Riscafe"). Not used anymore.
1.1.x - this was integrated into Netscape and Internet Explorer and therefore used for a long time in applets. The first implementation of Swing was based on 1.1.x and was distributed as a seperate package. Only seldomly used nowadays.
1.2.x - called "The Java 2 platform" by Sun. Acorn's new Java was planned to be a 1.2.x implementation, but was only nearly finished. Swing is included.
1.3.x - Sun started using the "Hotspot JVM" with this release, a dynamically-recompiling JVM
1.4.x - this is in some way important since 1.4.2 is the first Java where Swing uses "native peers" to draw its elements, to be able to mimik Windows XP Look&Feel. Additionally, assertions were added to the language. This is IMHO still the most-used version and the baseline spec for many targets (later JREs can be used of course to run such 1.4.x compatible software)
1.5.x - now the confusion starts...Sun calls this "Java 5". For the first time, interesting language elements were added like generics, type-safe enumerations and autoboxing. The Sun JVM introduces Class Data Sharing to reduce memory footprint and startup times (two sore points for Java Desktop usage)
1.6.x - consequently called "Java 6". The first version to look sensibly on the Vista Aero GUI