This is definitely not a statement of authority. It is not something which is conclusive. It is merely sort of an outline.
The distinction between the two, in simple terms, is often said to lie in the following:
1. If one is Aspergian, one is relatively proficient in the verbal realm, and relatively weak in the visual-spatial realm.
2. If one is HFA, one is relatively proficient in the visual-spatial realm, and relatively weak in the verbal realm.
I, myself, even though I would never have been diagnosed with Asperger's because of my extreme speech delay, exhibit an Aspergian profile--in that my Verbal IQ scores, consistently, are much superior to my Performance IQ scores. The difference has lessened over the years. But when I was 15, I took the Weschler (spelling?) test, and scored 150 Verbal, 90 Performance.