Currently, there is no clear cut definition of HFA, and it is not a diagnosis term, but more of a secondary term to further explain one's place on the spectrum. Many researchers/doctors argue that HFA & Aspergers are essentially the same thing, while others say there are clearly defined differences.
From my perspective, HFA can mean that whatever Autistic disabilities you have, you can still function at a high (often near NT) level, meaning you can take care of yourself, perhaps hold a job, drive, marry, etc. This in relation to someone "low functioning," who would possibly need full time care, does not communicate with the outside world, etc. As for Aspergers, well, a lot of ASD folks can indeed live a near NT lifestyle, while others are extremely limited by lack of any social skills or ability to relate to others. They may still be able to hold a job, live semi-independantly, but not be able to do everyday things, like shopping.
The Spectrum is indeed wide, and there is a lot of disagreement among the medical community about what is what, and who is where…
_________________
?No great art has ever been made without the artist having known danger? ~ Rainer Maria Rilke