A true HQI is a M80 ballast- Sunlight Supply Blue Wave 3+7, PFO HQI, Aquamedic HQI. They will drive HQI bulbs to their correct wattage, and overdrive bulbs that are not HQI.
Electronics will run most HQI bulbs, but will underpower them.
Easiest example is Radiums. Despite being mogul base, they are European bulbs, and are HQI. Icecaps(electronic) will run them, but not to their spec wattage. They will appear blue-er and have lessoutput and life because of it.
Run the Radium to its spec wattage with the M80 ballasts, and it will be very bright, more white, and last longer.
Run a normal 250w bulb on HQI, it will tend to be whiter, have more PAR, and it will significantly reduce its life.