If you’re sitting comfortably, I’ll begin.
Scale (the ratio between the size of a real engine and that of our models) is 16mm to 1 foot. Sorry about the mixed units, it’s always been that way in model railways.
That equates to about 1:19, so a model of a 19ft long locomotive would be 1ft long. Or about 30cm if you prefer.
For comparison, your good old Hornby OO model trains are 4mm to the foot, or about 1:76.
So our 16mm stock is four times longer, wider and taller than the same model in OO. Only most 16mm models are of narrow-gauge trains (think Ffestiniog or Lynton and Barnstaple) so a better comparison is with 009 stock.
Gauge is the distance between the inside of the rails. Standard gauge railways are 4ft 8 1/2in between the tracks, whereas narrow-gauge can be anything from 1ft to 3ft or so, with 2ft gauge being the most common.
In 16mm models, 2ft scaled by 1:19 comes to about 32mm (love those mixed units). So we mostly run on 32mm gauge track.
Some of us use 45mm track, because it approximates to 3ft gauge (as in Irish narrow gauge for example), because (arguably) the rolling stock is more stable on wider wheel-sets, or just because they prefer it that way.