Hi All
The three "standard" gauges came about for much the same reasons as in 4mm/ft; the commercial gauge was followed by attempts to get closer to the correct gauge. S3 to 14.125mm gauge was proposed by John Delaney and Stewart Hine in 1972, but as it involved manufacture of your own wheels it didn't get beyond the dedicated few. Somewhere around the same time Ken Garrett proposed 13.5mm gauge, using standards which enabled the use of commercial wheels from Sharman, Kean Maygib and others, and I believe that around that time the 3mm Society published similar standards (Intermediate Standard) for 12mm gauge, again to enable better running with those wheels, and to get away from the coarse Triang standards. I believe GeorgeM uses the Ken Garrett standards in 13.5mm gauge, while most current 12mm gauge modellers use the Society's Intermediate Standard.
A more recent and major change (late 1980's I think) came about when the Society decided to actively support 14.125mm gauge, and published their Fine Standards to form a basis. The support included developing a wide range of Fine scale wheels, and providing Code 60 rail (with chairs from member Ian Osborne); the Society now offers 14.125mm and 13.5mm track bases, and chairs for pointwork, with more components in the pipeline. Fine standards were also published for 13.5 and 12mm gauges; I don't know if anybody uses the former, but a few certainly use the latter.
As Chris Higgs said earlier, the Fine standards are more pragmatic than S3; they're almost identical to P87 but with a
slightly deeper flange. That makes them around 0.3mm overwidth. For inside cylinder locomotives this doesn't seem to be a problem; I've had to scrape out the insides of splashers on a couple of old whitemetal kits (which I wouldn't use these days anyway), but that's it; the Mitchell GWR 517 etched kit I built was very tight, but that's more the nature of that locomotive.With outside cylinder locomotives it depends; I've built a Mitchell Manor with no problems, but on a Worsley Works 42XX I had to drift the cylinders out a bit (not noticeable, to me anyway), even the GWR had to resort to dodges like recessed crankpins with that one.
So, in summary, apart from the dedicated Triang enthusiast, in practice the majority of modellers use 12mm gauge intermediate standards, there's a fair number using 14.2mm Fine standards, a few using 12mm Fine standard, and at the moment 2 or 3 using the 13.5mm Garrett standards, although interest in that seems to be increasing.
I've mentioned the Society Fine standard wheels. With the disappearance of the Sharman, Kean Maygib and Romford products, the Society has now introduced a broad range of wheels to RP25 code 79 standard, which are compatible with Intermediate standard but are a lot finer in appearance than the earlier commercial products; they use square-ended axles similar to Romford, which helps with quartering.
Hope that supplements what Kat and others have written.
Cheers
Nigel