Does anyone know the difference between the gages in model rail roading?

Gauge is in reference of the distance between the rails on a stretch of railroad track, while scale works like this.... O scale is 1/48th the size of the real thing... H.O. scale is 1/87th the size of the real thing.. S scale is 1/64th the size of the real thing... N scale is 1/160th the size of the real thing, and... Z scale is 1/220th the size of the real thing.... G scale has no real set number(that I'm aware of)and it's mostly used as a garden scale so those trains can run out doors.

Gauges are the the width between the rails, but does not mean the same thing that of scale. If you mean scale, this is general rule of thumb a Z locomotive is the length of a finger, N locomotive is a little larger, HO locomotive is the size of a forearm, O locomotive is twice the size of HO, and G locomotive is the size of, say, a 6 month old child.

No one seems to have mentioned 00 gauge which is 1:76 (4mm/ft)

The gages are the length between the rails. G gage is the largest scale and N scale is the smallest scale. HO is the most popular gage in the USA and the world. OO is the near equivalent of this.