Ok. Here's the whole thing in a nutshell, if in fact that's possible.
"G scale" is often used by many to refer to any train that runs on rails that are 45mm apart (see also: gauge, hence folks sometimes also say "G Gauge." This is different from other model railroad scales where the scale determines the gauge .... in this case, the scale was determined by what type of trains folks want to run on 45 mm gauged track.
As such, as you'[ve noticed, you've seen 1:20.3, 1:22.5, 1:24, 1:29, and 1:32 (among others) advertised as "G Scale" or "Large Scale" trains, and they're obviously different scaled models running on the same size track.
So ... here's how the sizes shake out:
1:20.3 -- the 45 mm between the rails represents 3 feet.... common for many American prototype narrow gauge railroads (Colorado, Alaska, SPNG, EBT, others.) Models in 1:20.3 are typically of this type of equipment, so if you're a fan of Colorado narrow gauge, this is the scale made for you. Note that of the ones I'm discussing, the actual models are the largest in size, proportionally because the scale is the smallest, so space can be a consideration!
1:22.5 -- the 45mm between the rails represents 1 metre. LGB of Germany made trains in this scale for a long time, representing European narrow gauge trains that typically run on 1 metre gauge track. This is where the first of the confusion comes, though, as you'll often see models of everything from 3' gauge prototypes (for example, LGB's 20550 White Pass and Yukon DL535E Diesels, and the 2-6-6-2 Sumpter Valley / Uintah mallets) to standard gauge (the F-7 and the AEM-7) which were all selectively adjusted, sizewise, to fit. There are a lot of folks who see this kind of statement as a criticism ... it's not .... I'm just trying here to explain why you might buy LGB "G Scale" trains with identical boxes, and have an F-7 and a 2-6-0 from the Colorado and Southern that couple together and run about the same way (though prototype fans would shudder at the thought.)
1:24 -- the 45mm between the rails represents 3.5 feet. If you're modelling "cape gauge" or Australian prototypes this is the correct scale for you! There are also a lot of 3' gauge and meter gauge prototypes modelled in 1:24 that simply adjust things to fit the slightly wider track ... in 1:24, the 6 inches too wide that the gauge is comes out to about 1/4 inch, which many folks don't notice, so they're cool with the slight scale discrepancy.
1:29 -- the 45mm between the rails represents 4'8.5" (Standard Gauge) but isn't quite mathematically accurate.... in fact, the actual gauge is off by about the width of a railhead or two, but it makes the models quite large, which many folks like, and the scale discrepancy is hard to see. USA TRAINS and Aristocraft make trains in this scale, and some LGB equipment is either 1:29, or close to it.... most of the models involved are modern locomotives and 1930-1960 era freight and passenger cars, though there are some modern cars available as well. There are also some later steam engines from both suppliers which are very nice, including a couple from USA Trains in cast metal, and a live steamer from Aristocraft. Accucraft/AML makes some equipment in this size also.
1:32 -- the 45mm between the rails represents 4'8.5" (Standard Gauge) and is mathematically correct this time (45mm x 32 = 4' 8 1/2 inches.) The models are smaller than their 1:29 cousins. Accucraft and MTH both make trains in this size, and all represent standard gauge prototypes. Sizewise, the models are the smallest .... a 1:20.3 locomotive will sit on the same track as a 1:32 locomotive, but a tiny 1:20.3 locmotive will tower over the largest 1:32 locomotive when placed side by side.
Confused? Hope not. The thing to do is pick the kind of trains you like, and then choose a scale that suits you. And, as shown, some manufacturers pick really small prototypes in 1:20.3 or really large ones in 1:22.5 with the idea that they'll be able to run next to each other and some people won't mind.... so there's no "rule" about what you can and can't run on your railroad. Some folks have "standard gauge" days and "narrow gauge days" on the same railroad... some just mix and match and to **** with the scale. Whatever floats your boat .... though I suppose that expression is less appropriate here than it is other places!
Scottychaos posted the best visual aid I've ever seen to the scale/gauge question awhile back.... and here it is:
Hope this helps!
PS. This post took me an hour and a half to get posted.... between phone calls, etc.... if twenty people have answered by now, I apologize!