Terminology
Strictly speaking, scale is the relation of the size of a model to that of its prototype, and gauge is simply the distance between the railheads.
However, within the modeling community the terms "scale" and "gauge" seem to have taken on very specific connotations. In many cases, the original "toy" trains were built of plated & lithographed tin and/or thick printed cardstock, making use of oversized wheels & couplings and running on track sections that were designed more for ease of use and robust service rather than pure fidelity of reproduction. Small or delicate details were often represented as simple graphics on the models or even omitted altogether. This style of modeling enjoys a large and enthusiastic following to this day, with a brisk trade in both vintage and contemporary models. Many annual public events are held to promote and proudly display fine examples of the genre. These "tinplate" works and displays are most often associated with the term "S gauge", perhaps because many of the early firms marketed their wares using this specific phrase.
As production methods and consumer tastes changed over the years, more accurately detailed models were made available by manufacturers and constructed by enthusiasts. In an effort to distinguish these efforts from the "tinplate" products, the term "S scale" has been adopted by the adherents of this "higher fidelity" approach. Examples of scale works are seen at many shows every year but, it must be honestly noted, there are fewer modelers in the 1:64 proportion than almost any other.
Read more about this topic: S Scale