As has been pointed out elsewhere in the thread of replies, the 3mm Society is a scale society and not a gauge society. As a result the Society's published wheel and track standards can appear confusing when set against those from P4, S guage or the 2mm Association. The easiest way to pick a way through the undergrowth is to think of the Society's standards being three sets of wheel standards.
The coarsest is the legacy Triang standard, set by Triang over fifty years ago when every railway model manufacturer thought trains were steamrollers on rails. The problem for the 3mm Society is that Triang did such a damn good job at the time making indestructible mechanisms and producing locos, coaches and wagons that were superior to their OO counterparts that a lot of Triang TT is still in use today. However, similarly coarse wheelsets are delivered by Continental TT manufacturers at least until very recently.
The next standard is the Society "Intermediate" standard. Not a very good name as it doesn't convey the fact that this is the more forgiving of the two wheel profiles used by the 3mm Society for the wheels they sell to members to use on the rolling stock they build. In the past wheels have been made to this standard by Chris Hardy, Romford, Kean-Maygib and Alan Gibson. The Sharman Millimetre range also fitted this profile. About four years ago the 3mm Society launched their own SQ (self quartering) range. These have a square axle hole for ease of quartering, and - more importantly - ensuring wheels stay properly quartered. Dimensionally these wheels are about 0.5 mm too wide for exact scale and the flanges are approximately twice as wide and deep as the exact scale equivalent. In proportion these wheels are only slightly coarser than 2mm FS are of a similar fine-ness as 7mm finescale and are a little finer than RP25. Or RP25 as was, the NMRA seem finally to have twigged that RP25 doesn't match their own wheel standards
The Society also drew up a Finescale wheel standard and through the 1990s produced loco and rolling stock wheels to that standard. The full range is still available to Society members. These wheels are correct scale width, albeit that the upper tolerance is about 10% over scale width, but flange width and depth are about 50% overscale.
The fact that 3mm Society finescale wheels are still a little overscale has led some people to propose an S3 standard, one where wheels and track are built to exact scale. The reaction of most 3mm Society members has been along the lines of "best of luck with that" and certainly the Society, nor anyone else, has not delivered any product to that standard.
All three wheel profiles have been used on different gauges
The legacy Triang profile, and its modern commercial TT relations, is really only for 12mm gauge though back in the 1980s a layout appeared in the model press where Triang wheels had been pushed out to allow the rails to be set 14.2mm apart. That approach is not recommended by the Society.
The Intermediate profile is intended for 12mm gauge though the Society will sell axles for the SQ wheels that allow them to be used on 13.5mm or 14.2mm gauge track. Track standards have to be tweaked however, flangeways widened, so that these wheels can pass through crossings. I personally have built a small test track with three points to 13.5mm gauge and using Intermediate profile wheels and it seems workable.
The finescale profile has been used with 12mm gauge but most of those who use the FS wheels also use an exact scale track gauge - 14.2 mm for standard gauge, 15.75mm for Irish broad gauge and 21mm for Brunel's broad gauge. George Mitcheson was building an ambitious 13.5mm gauge layout using the finescale wheel profile on his stock but I believe a change in circumstances has meant this project has been shelved.
As to what works, the best thing is probably to view some of these layouts at shows. At the Crawley MRS show this weekend there were examples of 12mm gauge using Intermediate standard wheels (Paul Hopkins' Redford Junction and Tony Briddon's Bilton Goods), 14.2 mm gauge using finescale wheels (Peter Bossom's Whatlington and the Croydon MRS' Hemyock) and 15.75 mm gauge using FS wheels (Ballyconnell Road). All fine layouts demonstrating what is possible in 3mm scale.
There will be similar pods of 3mm scale layouts at Wells and Warley later this year, showing the different ways of modelling in the scale and in October, in conjunction with Worsley Works there will be a 3mm scale only show in Kidderminster.
Hope this helps
3mm Society Chairman