Size matters, right? Truth is, they're all O scale. The difference is track gauge. Track gauge is the spacing between the rails - from inside rail to inside rail.O gauge, On30 gauge, and On3 gauge, are all O Scale (1/4 inch equals one foot).
O gauge is 1.25 inches between the rails (inside rail head to inside rail head). O gauge represents prototype standard American railway gauge modeled in O scale, that ran on prototype track spaced at 5 feet between the rails.
On30 or originally On2.5 foot gauge is 0.65 inches between the rails (the same gauge as HO scale track). On30 represents prototype narrow gauge modeled in O scale, that ran on prototype track spaced at 2 feet 6 inches between the rails.
On3 represents prototype narrow gauge modeled in O scale, that ran on prototype track spaced at 3 feet between the rails. On3 gauge is 0.75 inches between the rails.
Simple, right? You see the problem is when you set down real prototype railroad ties and then nail in rails, you can put parallel rails as close or as far apart as you like. It depends on the distance between the wheel flanges on the rolling stock and locomotives you want to run on your railroad. There wasn't a standard gauge in this country for a long time. It didn't matter at first, because you ran your own stuff on your own railroad. Once railroads started sharing equipment and service routes, it became an issue. It gets even more complicated if you want to use European gauged equipment and track.
Just remember, Scale, is the modeling dimension - 1/4 inch equals one prototype foot in O Scale. Gaugeis the width of the rails. O, On30, and On3 gaugeare all O Scale models that run on different gaugetrack.