According to my information, the HS version is supposed to have faster focusing than a non HS version, (but I don't know just how much faster that would actually be).
There were four remodelled lenses up to HS versions in the list I have.
It says: They were redesigned in 1988 for Maxxum Series-i cameras. Internal changes include a faster gear and a new IC ROM to enable faster focusing with Series-i, xi, and si cameras.
External changes include AF lock/lens function button (one for 200mm, two for 300mm and 600mm lenses), and "High Speed Focus" decal on the lens shade.
Additionally, the 80-200mm f2.8 APO recieved a stronger focusing shaft which enabled better focus tracking, a rubber focusing grip for easier manual focus, and white paint finish.
There is also a warning footnote, that the APO converters cannot be used with the 80-200APO lenses, the front element of the converter will contact the rear element of the lens and both will be damaged.