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Oh boy. As you would expect, there's lots of variables that come into play. The pin and plug have to meet the needs of the voltage and amperage that they will carry. Pin spacing will also be affected by the size of the traces and their spacing that the pins will attach to on the circuit board. Beyond that, it comes down to the preferences of the manufacturer.
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The only "standards" for the most part are set by the specific manufacturer, for a specific product line. There literally thousands of product lines in current use, and tens of thousands more historic lines that are no longer made. As you can see here at a popular parts supplier in the US:
https://www.digikey.com/en/products/category/connectors-interconnects/20
there are over 5 million separate results searching for "connector". That is FAR from a comprehensive list. There are hard metric, hard English pin size/spacing's and a few that are "both" meaning close to an even mm dimension and an English dimension that is an even fraction of an inch. Sizes range from so tiny you cant see the individual pins to huge (for high power AC distribution for example), depending on application. By convention the headers on mother boards are .1" spacing (both ways if multiple rows). The shroud (with or without key slot) is optional and often omitted as a cost saving measure. these are a significant improvement over edge card connections, but still not exactly "safe". The pins are always square and "tinned (coated or plated with metals similar in appearance and possibly composition to solder)" or gold plated, which effects reliability, cost, and capability (voltage and current specs). The mating female connectors come in a variety of sizes, and internal construction in turn effecting cost and performance. MOST of an EE's job in the modern world is about selecting parts for availability, spec, cost, etc. EVERYTHING is tradeoffs: cost vs performance vs thermal management vs ease of use/manufacture etc. etc.
Every manufacturer thinks their products are superior - and maybe they are in some applications. Nothing works well everywhere. Some (like 0.1" pitch headers) are more common than others. Even in specialized applications like RF there are dozens of kinds in common use, all have their pluses and minuses. And a hundred more that are very uncommon and found only in certain applications or in certain countries products.
Using the latest technology to create tomorrows problems today.
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I believe the connector variety you're looking for was originally manufactured by Dupont. They are called Dupont connectors these days.
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One of the better innovations I've seen in PC building was what ASUS calls a Q-connector.
You don't futz with all the connections directly on the board nor the manual to map them. They provide a block that covers the 12-16 pins all at once. You plug stuff into the block where each pin is labelled, then put the whole block on the board.
I'd guess there'd be something of a market for that sort of thing in a bunch of other hardware too.
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More convention than standard. There are standard connector types, most started as some manufacturers spec, 0.1" square spacing double row the most common, usually square pins, ( this is mostly a manufacturing consideration, especially related to how the female contacts are made - stamped from thin sheet), but 0.157 (? that's from foggy memory ) isn't that rare, and the dreaded 0.2mm ones are used when some bright eyes wants to save a tiny bit of space.
Higher power connectors usually mean larger pins, wider spacing, often round pins ( to match more robust machined sockets ).
The other convention, that Rasp Pi violates in the name of price, is that power flows out of female connectors.
( Yeah, I blew up one Pi when the pins touched a piece of EMT. )
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Thanks to everyone who replied to my request.
I guess some of you wonder why I asked the question, and was so eager about the formal standard. I'll tell:
A while ago, I got so frustrated over the enormous numbers of 'standards' I (have to) relate to (ref. Tanenbaum: The good thing about standards ), that I sat down to make survey of 'Standards I Have Met'. I went though a large number of areas, from storage media to lightbulb sockets to battery cells to SCSI plugs (my equipment used 8 different ones - but there is said to be 14 ones in use) before I ditched SCSI), USB plugs (one more now, and I will be tempted to let USB go the same way as SCSI), ... I also made sections of software standards I have tried to adhere to, such as document formats, character encodings, binary numeric formats etc.
In almost every every, there were so many 'standards' that it turned my frustration into fascination. I never thought there would be that many! So I decided to try to make the list as complete as possible. I took a look at my PC mainboard to see which I had forgtten (I put my PCs together from separate parts, so I do relate to the 'standards'), and asked about the standard for these front panel(++) headers to get it into my list. I guess they go into my list as something like 'Unidentified standard(??) #27'
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Back in my younger days we had these same pin's on the underside of the BBC Micro, and the sockets, slots variations on devices etc.
The standard they where known by, along with the ribbon cables that attached them where
"IDC Connectors"
Sometimes single row, sometimes double, some where male, some where female, some where 10 pins long, others where 20 pins or more, then there was the flat ribbon cables and the square plugs that went on the end, we just called all of them by the same name.
These days, I have a crimping tool and pins/sockets rows, double blocks, 1x2 2x1, 2x2, 4x2 and so on...
Those wires and connectors (According to my crimp tool manual) are called
"Dupont Connectors"
Dunno if that's the info your looking for.
Shawty
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I'll stick with software development; sitting around drinking coffee and not having to track down who misplaced my wrench.
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And it's really difficult to skin your knuckles on a sharp* bit of code!
* Or even a C# bit of code.
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony
"Common sense is so rare these days, it should be classified as a super power" - Random T-shirt
AntiTwitter: @DalekDave is now a follower!
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Depends on how hard you bang your keyboard.
Give me coffee to change the things I can and wine for those I can not!
PartsBin an Electronics Part Organizer - An updated version available! JaxCoder.com
Latest Article: Simon Says, A Child's Game
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Come, come now, there are young people watching. 
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Richard MacCutchan wrote: Come, come now, there are young people watching.
Uhh...I'm pretty sure there are no young people here. 
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Whaddya sayin'? I only turn 62 next week. That's young enough.
Software Zen: delete this;
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I'm young in that case... 50 here
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True story: Back when I was in college I worked at Wright-Patterson Air Force Base on a VAX-11/780, which used DEC VT100 terminals.
I broke a VT100 keyboard by banging on it too hard.
Software Zen: delete this;
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I've hit mine pretty hard, in the past but never broke one.
Give me coffee to change the things I can and wine for those I can not!
PartsBin an Electronics Part Organizer - An updated version available! JaxCoder.com
Latest Article: Simon Says, A Child's Game
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I've broken my knuckles once, but not the keyboard...
That said that was a bit more force than just banging the keyboard, it was more of a sustained beating I was giving the thing, a bit like when the good guy finally catches the bad guy and has him on the floor explaining the error of his ways 
Yea, I really lost my temper that day!!!
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I've been close to that point but got up and walked away.
Although I've destroyed 2 cell phones in a fit of rage. The Ex knew just what buttons to push!
Give me coffee to change the things I can and wine for those I can not!
PartsBin an Electronics Part Organizer - An updated version available! JaxCoder.com
Latest Article: Simon Says, A Child's Game
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ha ha yes....
I used to have a one of those windows mobile 6 smartphones, with the slide out keyboards, and it was the perfect size and shape for my wife to throw!
She's not got a very good throwing arm, but that one device she could throw and hit her target bang on every-time.
Every-time I upset her, or we had a tiff, the first thing I used to do was pick my phone up and hide it, or put it in my pocket where she couldn't get a hold of it, damn thing was also solid enough that it hurt like hell when it hit you!
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Aye, I've seen those things!!!
Friend of mine used to have a vinyl sign cutting business, he had an A3 cutting/plotter thing that you fed vinyl into the back of by the roll and it whisked around at high speed cutting out complex shapes, damn thing was terrifying.
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PIEBALDconsult wrote: not having to track down who misplaced my wrench.
So how do you deal with the person who broke the build a day before the planned release? 
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows.
-- 6079 Smith W.
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