| In Europe the most common mains voltage is 220..240V, in the US (or more generally North America) 120V. That is, where the differences start.
The 220..240V is quite sufficient to run 100..140V arc (lower limit for wattages, as the higher current arc tend to be more stable even with less OCV margin) with just a series choke, so suffice with a simple, very efficient, cheap and lightweight ballast. So therefore all European lamps are designed to fit into that voltage limit over their complete life cycle. As the HPS increases it's arc voltage over it's life, they are designed with the initial voltage somewhat lower, in the range of 70..100V (again, lower power means lower voltage, higher power higher voltage)
Some models with 1kW and above with arc voltages up to 200V, which then run on 380..400V readily available between phases in the common 3-phase system most common in Europe. Such power would require 3-phase connection anyway, so again the simple, relatively cheap and efficient series choke.
In the US the 120V would impose an upper arc voltage limit of about 70V at the end of the life, so about 55..60V initially. That would yield rather short, high current arc, so rather inefficient lamps. Therefore (except really low wattages) the lamps would need a transformer to boost the voltage up. But once the transformer is there anyway, neither complexity, nor cost, nor efficiency would then depend on any exact voltage the transformer would be designed for. So that mean whatever OCV the lamp needs, the ballast cost, losses and weight would be about the same. That makes the situation a bit different from the Europe: The lamps were then optimized for the highest efficacy attainable from each given power level. This optimization took into account the ballast losses as well, therefore the low power (150W S55 and below) ended up as "55V", to be operated on just a series choke ballast. But from S56 150W and above the arc voltages are higher.
So with an exception of the S56 (there the optimum happened to be so close to the European requirements, so it was designed to be really equivalent), none of the HPS matches it's European counterpart.
With the MV the situation was a bit different: The MV technology started in England in the form of the medium pressure "Osira". As it was in England, the 240V offered good OCV for a reasonable 130V arc with just a series choke, so the 100..140V arc become a standard for the MV's since then, even when the technology spread over the ocean. There it required a transformer, but as the first lamps were imported from the UK, the standard was set.
And as the 100..130V was a standard, it sustained like that even till the probe start metal halide, so they were made (in the US, as these came from there) according that spec as well, the original intention was to operate them on a regular MV gear. Very soon the experience came, the OCV had to be increased (that was no big deal, as the transformer was necessary anyway), so the MH gear was respecified. But the new spec's kept the gear still compatible with MV's, so the original aim (MV-MH compatibility) was still kept.
But in Europe the need for extra OCV was a complication, as that would mean the need for way more lossy, heavier and expensive transformer ballast, what made that technology not viable (the extra efficacy would be lost in the higher ballast losses).
A solution came in the form of a voltage pulser, an ignitor: The extra voltage was necessary just for the initial arc ignition.
But when the ignitor become required, it was of not much difference, if the ignitor supplied just a bit extra for the US probe start lamps, or generated real hig h voltage pulses to start the lamps without the otherwise troublesome starting probe (it tend to damage the quartz by an electrolysis, therefore the need for the bypass contact in the lamp; and it requires the seal to be physically larger, so loose way more heat in that critical area). So a pulse start MH lamp concept was born.
Now as the HPS arrived at similar time and it was the fact the HPS needed the ignitor as well, an idea popped up to make the pulse start MH's compatible at least with the HPS. But the European ones, as in the US the pulse start system was not needed, the probes worked well.
The simpler seals then allowed the design with very high arc loading, eventually with ceramic arc tubes, what opened the room for more efficient fill cocktails of the lamps marketed today.
And as the pulse start MH concept came from the Europe (from the necessity) and it turned out to be an advantage (efficacy, color quality,...), it was exported back to the US, but as with the MV's half a century ago, it bring the standards with it. So the pulse start MH's become, similarly as the MV's, compatible between the US and European market. Of course, there is no compatibility between MV and MH...
So I hope it was understandable at least a bit...
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