AQI = Air quality index
AQHI = Air quality heath index
The AQI reports the current quality of the air relative to the measured amount of pollutant. It can be simply stated as the report that the government is giving to the public on how polluted the air in a specific surrounding is and will be in the next two/three days.
AQHI on the other hand is a report on how the air quality affects human health. This is a sort of warning the people on the impact of air pollution to one's health. It has a scale of 1 - 10+. Scales below 4 are considerably good conditions to stay outdoors. Scales of 4-6 has a moderate risk. Ratings above 7 is considered high risk and should be avoided as much as possible.