From what I have seen, 250W mercury vapor lamps seem to all have virtually identical electrical specifications no matter which country they are being sold to and the same applies to 400W mercury vapor lamps being sold across virtually every single country. I think one major factor is that most countries in the world adopted European specific lighting equipment.


Interestingly, I have been seeing that both Japanese 250W mercury vapor lamps and North American 250W H37 mercury vapor lamps all have virtually the same electrical specifications to the European 250W mercury vapor lamp while both Japanese 400W mercury vapor lamps and North American 400W H33 mercury vapor lamps all have virtually the same electrical specifications to the European 400W mercury vapor lamp.

Shown below are some spec sheets for the 3 different types of 250W mercury vapor lamp standards:

North American 250W H37 mercury vapor lamp:

https://www.iesbuy.com/ASSETS/DOCUMENTS/ITEMS/EN/Philips_Lighting_248146_Datasheet.pdf

Arc voltage drop: 135V
Operating current: 2.1A

European 250W mercury vapor lamp:

https://www.bright.gr/eshop/uploads/files/2017/02/philips-hpl-n_250w_542_e40_hg_8682.pdf

Arc voltage drop: 135V
Operating current: 2.1A

Japanese 250W mercury vapor lamp:

https://www.iwasaki.co.jp/data/discon/HF250X/10/0001888.pdf

Arc voltage drop: 130V
Operating current: 2.1A

Shown below are the spec sheets of the 3 different types of 400W mercury vapor lamp standards:

North American 400W H33 mercury vapor lamp:

https://images.salsify.com/image/upload/s--f5zI33Px--/84209aa0d5c73a826db2cd54f38a5b835eb74b89.pdf

Arc voltage drop: 140V
Operating current: 3.25A

European 400W mercury vapor lamp:

https://goactive.nz/storage/media/2020/10/1602703642-928053507496-euen-nzproffp.pdf

Arc voltage drop: 140V
Operating current: 3.25A

Japanese 400W mercury vapor lamp:

https://www.iwasaki.co.jp/data/discon/HF400X/10/0001890.pdf

Arc voltage drop: 130V
Operating current: 3.30A

Why is it the case that virtually all of the world’s 250W mercury vapor lamps were made to be electrically interchangeable with each other no matter which country they were sold to?

Additionally, why were virtually all of the world’s 400W mercury vapor lamps made to be electrically interchangeable with each other no matter which country they were sold to?

Surprise, if something was done properly in this screwed world

These were the first wattage specs, created in GB for the early MA medium pressure lamps. At that time with the MA technology did not make sense to make anything smaller than 250W, as the system efficacy won't be any improvement over then standard incandescents, so the MA range stopped there.
At the same time the 400W was about the highest output needed in large quantities for street lighting (as that was the only application that tolerated the very low light quality), so the "mainstream" offerings ended up with just these two wattages.
The US market just started importing the lamps, so the same spec took home in the US as well.

Later on, when the quartz processing technology was developed to become competitive in lighting business, high pressure lamps came to the mass market.
But this development was to some extend done rather independently in the US and in Europe, so although with MV some synchronization still took place to some extend (same wattages had the same specs), the markets start departing from each other, so different wattages became the mainstream products in the US (175W, 100W) vs Europe (125W, 80W).
Then with the newer technologies (MH, HPS) the specs were very different, but that was steered mainly in the difference in characteristics of the most common ballasts used in each market (CWA in the US, strictly series reactor in Europe), so the specs were optimized to reach the highest system efficacy in the given environment (120V mains dictates a step-up transformer for anything above 150W so the voltage/current specs leading the maximum efficacy were selected, where the 230V still sufficed with a way more efficient series choke ballast, so for higher power lamps the lamp arc voltage became restricted by the 220V mains as OCV, with lower power lamps the arc voltages were increased to reduce ballast losses from the same 220V OCV).

MH became separate as the higher OCV of the US MV CWA ballasts allowed to start then seemingly simpler probe start lamps so avoid the need for an ignitor and allowed to operate them in the same systems as MV.
But the European 220V was too low for that, so the lamps would need an ignitor anyway, making the system more complex and breaking the MV compatibility.
So if the ignitor was needed and compatibility with MV imppossible anyway, Europe moved directly to simpler pulse start lamps. And adopted the MH later, at the time when HPS systems started to spread. So many MH specs shifted for HPS compatibility instead, as the system requirements were very similar (series choke ballast, an ignitor).
And many used a kind of "middle ground", took the ballast choke from MV and an ignitor from a HPS system. The reason for this is, most MH systems do not need as high OCV/arc-V ratio as the HPS do (no more than about 80..90V arc for 220V OCV), but allowed way higher arc voltage similar to MV (100..140V for the 220 mains), so allowed lower currents so ballast losses. It did not create any extra logistic problems, as the ballast components were distributed separately anyway, so asking for combining an "MV choke" and a "HPS igniter" for the given MH ballast was not a big deal.

Although Japan seemed to have a range of unique wattage mercury vapor lamps available like the 200W and 300W ratings, I have noticed that the 250W and 400W lamps seemed to also have similar specifications too. So, why did Japan adopt these established mercury vapor lamp specifications for their 250W and 400W lamps?

Because in the medium pressure MA era these were the only two wattages made. And because they came from a single origin (UK), the spec is the same.
And once such standard is set, it stays forever...