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