One needs to be careful with the term HQI, as it has to different means in light bulbs
HQI = Halogen Quartz Iodide
HQI = Mercury ( Hg, - the g) Quartz Iodide
The first one usually is associated with special high output incandescent lamps, some times called Tungsten Halogen. Many of these lamps are double ended just like the Euro HQI. You have seen them before in hardware stores. They are about the size of a cigarette and are often used for outdoor lighting
Halogens
Here is how the bulb works.
HQI Tungsten Halogen
Here is what the double ended bulb looks like, bottom of page
Halogen doulbe bulb
The Euro HQI, is a double ended MH. Both types of HQI look somewhat similar but work completely different. Here is an intro
Aquarium Lights
As you can see from the diagram the double ended Euro HQI do not have the large outer envelope that the std tubular or elliptical MH have. They operate basically the same. Mercury is found in all HID lamps. The Quartz, is that the tube is mad of quartz, usually Borosilicate.The Iodide comes from on of the Iodides used to produce light, along with the Mercury and Argon gas. The Iodides are usually of rare earth soft silver metals;
Scandium Iodide, Thorium Iodide etc. The combination of these Iodides gives the lamp characteristics you want
Iodides
Metal Halide Operaiton