Julius is a high-performance, two-pass large vocabulary continuous speech recognition (LVCSR) decoder software for speech-related researchers and developers.  You need to have a Statistical Language Model and an Acoustic Model for your language to run the recognizer.  It is used in dictation applications.

Julian is a modified version of Julius which performs Grammar-based recognition (i.e. it uses a Grammar, rather than a Statistical Language Model to perform recognition).  The Grammar describes possible syntax or patterns of words to perform a specific dialog task. When given a speech input, Julian searches for the most likely word sequence under constraint of the given Grammar.  Grammar-based recognition is used for command & control type applications on desktops, or for telephony IVR type applications.