The Steam version is automatically updated by Steam, where the website version will offer a link to an installer you can download and run.
Other than that, the only real difference for VoiceAttack itself is the license and license verification system.
The Steam version requires Steam to be installed, but once activated (which is normally done automatically the first time the application is started), doesn't require Steam to be running, if VoiceAttack's executable is started directly.
Instructions for creating a desktop shortcut to the executable can be found
here.