So here is the story: inside NASA, "Deep Space" used to mean (prior to 2003) anything beyond the orbit of the Moon. This was intended to be the domain of work for science and telecommunications ops of the Jet Propulsion Laboratory (JPL), an FFRDC operated by Caltech as a NASA center. Inside the Moon's orbit was the domain of scientific work for NASA's Goddard Space Flight Center (GSFC). This included Earth observing science and telecom as well as astrophysics spacecraft. During the Constellation program, when simply returning to the Moon was not enough justification for the program and seeking a way to justify control of the design of deep space telecom for manned spaceflight, the Constellation Program Office at NASA Johnson Space Center (JSC) and NASA GSFC sought to redefine deep space as anything beyond HEO. This was also an attempt by GSFC to put JPL's Deep Space Interplanetary Network (aka "DSN) on the sideline of the design process for Constellation deep space telecom. (Furthermore, GSFC at the time was lobbying to get new Earth orbiting telecom spacecraft launched and needed additional justification, ergo "they are good for Constellation"). I don't think the issue was every resolved one way or another as far as "official" definitions go and in the end, not much changed before Constellation was cancelled. The lesson is this: Words like "deep space" can mean a lot when government research centers are fighting to protect their charters and business base. I'm glad I'm out of that biz!