Usually at big shoots, what I have seen is HAA is the person who scored the best cumulative score for the "big 3 events," that is, Event Singles championship (usually 200 targets) Event Doubles championship, and the Event Handicap championship.
Its usually delineated by your singles classification, that is, there will be an Event HAA champ, and Event HAA runner-up, Class AA HAA champ, Class A HAA champ, etc.
A perfect HAA score is usually 400.
HOA is often a the cumulative score of a larger number of events, usually 8 or 10 events comprising of preliminary events and championship events. That's why you'll see HOA totals in the thousands.
In order to score well in HOA, you have to enter all of the preliminary events.
Others may have more to add.