AGS and GIA are not grading the same things. Each has a list of standards for what is required to qualify for their top grade and there are certain stones that will meet both but there are also quite lovely stones that will meet only one, or neither. Unfortunately, it's not as easy as people would wish. Use the search box to look for threads on 'GIA cut' and 'AGS-0' and you'll find quite a bit of discussion on both systems as well as what the differences are.
Both systems involve some attributes that aren't part of the HCA and both labs reserve the right to final say on the grading, which is the reason that it estimates 'candidates'.