linguistic:paraphrasing, linguistic:translation
Gauge vs scale

Model railroads originally used the term gauge, which refers to the distance between the rails, just as full-size railroads continue to do. Although model railroads were also built to different gauges, standard gauge in full-size railroads is 4' 8.5". Therefore, a model railroad reduces that standard to scale. An HO scale model railroad runs on track that is 1/87 of 4' 8.5", or 0.649" from rail to rail. Today model railroads are more typically referred to using the term scale instead of "gauge" in most usages.

Confusion arises from indiscriminate use of "scale" and "gauge" synonymously. The word "scale" strictly refers to the proportional size of the model, while "gauge" strictly applies to the measurement between the inside faces of the rails. It is completely incorrect to refer to the mainstream scales as "HO gauge", "N gauge, "Z gauge", etc. This is further complicated by the fact some scales use several different gauges; for example, HO scale uses 16.5 mm as the standard gauge of 4 ft 8 + 1 ⁄ 2 in (1,435 mm), 12 mm to represent 1,000 mm (3 ft 3 + 3 ⁄ 8 in) gauge (HOm), and 3 ft 6 in (1,067 mm) (HOn3-1/2), and 9 mm to represent a prototype gauge of 2 ft (610 mm).

The most popular scale to go with a given gauge was often arrived at through the following roundabout process: German artisans would take strips of metal of standard metric size to construct their products from blueprints dimensioned in inches. "Four mm to the foot" yielded the 1:76.2 size of the British "OO scale", which is anomalously used on the standard HO/OO scale (16.5 mm gauge from 3.5 mm/foot scale) tracks, because early electric motors weren't available commercially in smaller sizes. Today, most scale sizes are internationally standardized, with the notable exceptions of O scale and N scale.

There are three different versions of the "O" scale, each of which uses tracks of 32 mm for the standard gauge. The American version follows a dollhouse scale of 1:48, sometimes called "quarter-gauge" as in "one-quarter-inch to the foot". The British version continued the pattern of sub-contracting to Germans, so, at 7 mm to the foot, it works out to a scale of 1:43.5. Later, the European authority of model railroad firms MOROP declared that the "O" gauge (still 32 mm) must use the scale of 1:45, to allow wheel, tire, and splasher clearance for smaller than realistic curved sections.

N scale trains were first commercially produced at 1:160 scale in 1962 by the Arnold company of Nuremberg. This standard size was imported to the US by firms such as the Aurora Plastics Corporation. However, the early N-scale motors would not fit in the smaller models of British locomotives, so the British N gauge was standardized to allow a slightly larger body size. Similar sizing problems with Japanese prototypes led to adoption of a 1:150 scale standard there. Since space is more limited in Japanese houses, N scale has become more popular there than HO scale.