NMRA (National Model Railroad Association) standardized the first model railway scales in the 1940’s. NMRA standards are used widely in North America and by certain special interest groups all over the world. To some extent NMRA and NEM standards are compatible, but in many areas, the two standards specify certain model railway details in somewhat incompatible ways for the same scale.
There are two NMRA standard sheets where the scales have been defined. NMRA standard S-
In certain NMRA scales an alternative designation is sometimes used corresponding the length of one prototype foot in scale either in millimetres or in inches. For instance, 3.5 mm scale is the same as HO. For HO and O -
NMRA has defined alternative, more prototypical, track and wheel system standards in standard sheet S-
Proto scale was originally developed by the Model Railway Study Group in Great Britain in 1966.
This was later adopted into NMRA standards with modifications necessary for the North American prototype railway standards. Proto scale reproduces faithfully the prototype wheel tread profile and track work used by the Association of American Railroads and the American Railway Engineering Association.
Finescale reproduces the prototype wheel tread profile and track work used by the Association of American Railroads and the American Railway Engineering Association with minor compromises for performance and manufacturing capabilities.
'G Scale' and 'G Gauge.
Their are many groups and organisations supporting “G” Scale and “G” Gauge so we will leave it to the individual to decide on his or her preference. The Wikipedia article is a nice starting point with links to many modelling organisations. Below is the NMRA Guide on Deep Flange Scales.