AUD (App Update Detector) is a program for Mac OS X 10.9+ that detects for updates for any program that uses the Sparkle framework. This scans in the /Applications folder.
"Installed Short Version" and "Newest Short Version" are typically the human-readable version identifier, for example "2.1.4" or "1.2". The non-short version are usually for the developers or the computer.
There really is nothing fancy behind this, all this does is compare the installed version to the newest version or the "Installed Short Version" to "Newest Short Version" and see if they match.
If AUD does not find a newest short version, it will either return nothing or "<null>".
Icons8 for the toolbar icons.