A more complicated interpretation. Max's War and Peace time. Just a personal opinion. Settle back.
"G" is not a gauge, or a scale for that matter. However, it is usually a general "catch all" description applied to loco's and rolling stock built to run on 45 mm gauged track systems that use a chunky "code 332" rail (= rail height 332 thou"). Like LGB's , Bachmann's, USATrains' and other compatible makes.
Models built to operate on this type of 45 mm gauged track can usually be anything from 1:13 to 1:32 in scale. These scales can be expressed either as a ratio, e.g. 1:19.3 or as so many mm or fractions of inches needed to express a linear foot modeled, e.g 16 mm (to the foot) which as a ratio = 1:19.3, what a coincidence. The latter expression here is used for ease and its accuracy. Scales can also be represented by a letter, in the US primaraly, e.g. F = 1.20.3, which = 15mm to the foot. This letter can be applied to any gauge of 1:1 prototype for scaling. A letter type scale definition can then be followed "n" to denote a narrow gauge prototype being represented and then numerals to denote this prototype's actual track gauge, e.g. 3 for 3ft, e.g. Fn3 = a 15mm scale model of a prototype that runs on 3ft gauge track.
It should be noted that a model running on 45 mm gauged track may not have a scale correct gauge represented by the model, even though a scale and gauge is quoted. Infuruating, isn't it ?
Whereas, 16mm is not a track gauge, at least in garden rail terms as used here. It's a scale, see above. It is a recognised scale too, generally used to model locos and stock, in it's purest and originaly intended form, that would have run on 2 ft gauged track. As a result the correct track system for these models is 32mm (2 × 16mm to 1ft = 32mm). And a lot less chunkier rail. See above for this scale's definition.
However, the 16mm scale product manufacturers wanted to maximise sales and so made their items available to run on not just 32mm track systems but 45mm too. There are a lot more 45mm track based layouts and buyers about. So most product sold as "16 mm scale" is actually supplied gauge adjustable or ready set to work with either 32mm or 45mm gauges. But not all popular narrow gauge railways, in the UK and its former colonies were 2ft. And as a result the hobbyists wanted models of those that ran on diifferent narrow gauges, within reason, too. So,16 mm is a scale that is now used to represent anything from 2ft - 3ft gauged prototypes. To cap it all a lot of "16mm scale" products have no real life prototype, they are a figment of someone's imagination, so they are known as "freelance" models. You will see the term SM32 and SM45 bandied about, SM = 16 mm, nominal scale model built to, the numerals 32/45, the track gauge in mm they are built for. So you could have a model a 3ft gauged prototype, that would normally be reproduced in 15 mm scale to be true to guage at 45 mm, refered to as Fn3, actually modelled in 16mm that woulld be defined as SM45. Help !
It follows that "16 mm Scale" is as much a misnomer as "G Gauge" is, its all a scam to get us punters to shell out £€$'s. P.S. 16 mm scale is a British thing really, the Europeans use 1:22.5 mostly for similarly narrow gauged prototypes.
Confusing, infuriating ? Yes, catches us all out. Depends on how much of a purist you want to be and where you are coming from. Me ? I run Fn3 and 16mm scaled models, of actual prototypes (with one or two exceptions) all on 45 mm gauged LGB type track. And relax ! Max