What is the difference between versions of Eclipse (Europa, Helios, Galileo)? Which is the best for desktop application?
The Eclipse (software) page on Wikipedia summarizes it pretty well:
Releases
Since 2006, the Eclipse Foundation has coordinated an annual Simultaneous Release. Each release includes the Eclipse Platform as well as a number of other Eclipse projects. Until the Galileo release, releases were named after the moons of the solar system.
So far, each Simultaneous Release has occurred at the end of June.
Release Main Release Platform version Projects Photon 27 June 2018 4.8 Oxygen 28 June 2017 4.7 Neon 22 June 2016 4.6 Mars 24 June 2015 4.5 Mars Projects Luna 25 June 2014 4.4 Luna Projects Kepler 26 June 2013 4.3 Kepler Projects Juno 27 June 2012 4.2 Juno Projects Indigo 22 June 2011 3.7 Indigo projects Helios 23 June 2010 3.6 Helios projects Galileo 24 June 2009 3.5 Galileo projects Ganymede 25 June 2008 3.4 Ganymede projects Europa 29 June 2007 3.3 Europa projects Callisto 30 June 2006 3.2 Callisto projects Eclipse 3.1 28 June 2005 3.1 Eclipse 3.0 28 June 2004 3.0
To summarize, Helios, Galileo, Ganymede, etc are just code names for versions of the Eclipse platform (personally, I'd prefer Eclipse to use traditional version numbers instead of code names, it would make things clearer and easier). My suggestion would be to use the latest version, i.e. Eclipse Oxygen (4.7) (in the original version of this answer, it said "Helios (3.6.1)").
On top of the "platform", Eclipse then distributes various Packages (i.e. the "platform" with a default set of plugins to achieve specialized tasks), such as Eclipse IDE for Java Developers, Eclipse IDE for Java EE Developers, Eclipse IDE for C/C++ Developers, etc (see this link for a comparison of their content).
To develop Java Desktop applications, the Helios release of Eclipse IDE for Java Developers should suffice (you can always install "additional plugins" if required).