What do their HQL, HQI, HIT, HCI acronyms mean?
Also they have three distinct lines of Metal Halide bulbs:

POWERSTAR, POWERARC and POWERBALL.

For example, in my personal collection there is a POWERARC HIT-T 1000W/D bulb.
But it seems like this same bulb has a POWERSTAR variant.

How are they different?

@James site to the rescue   https://www.lamptech.co.uk/Documents/M4%20Nomenclature.htm

C second letter seems to be a modern addition, looks logical for Ceramic.

HIT is BLV (or some Chinese off-brand?) nomenclature, not Osram's.

PS:

HIT-T does exist, indeed. I think it is modern Ledvance addition for Chinese-originated lamp. Note NON-EU mark in the datasheet. May be a special non-European out-of-prohibition series for the rest of the world.

I have an Osram Powerarc HIT-T 70w (bi-pin G12, quartz MH) made in China.
https://www.lighting-gallery.net/gallery/displayimage.php?pos=-251627

In the beginning their metal halides were called “Power Stars”.  That was abbreviated to “Powerstar” but it seems not in USA, where the name was perhaps already registered.  Osram therefore introduced the brand Powerarc.

Powerball was introduced around 1997 for ceramic metal halide lamps with ball-shaped arc tubes.