I think you may be confused by the basics; your underlying assumptions are very wrong.
Firstly the earth is not round and the lines of latitude and longitude are not fixed, they are centred in many different places in the centre of the earth as a best fit for each of the various local datums and can be up to hundreds of metres out. So, no matter where you are their exact location depends on which datum you are on.
And you still haven’t said which local datum you are using so it’s hard to be specific.
If you are using global datum WGS84 then it’s not accurate at all, its averaged over the world and not directly meaningful in any one area. Everything is continually moving under it. OK for basic navigation but no good for accuracy. It’s a virtual GNSS reference frame about which the satellites orbit, and on which all the accurate local datums are linked.
Have a good read of this: [Only registered and activated users can see links. ]
An extract here: “The International Hydrographic Office and many international navigation systems quote the datum they use as simply WGS 84. As we have pointed out, this is, strictly speaking, insufficient for a datum. The version of WGS84 is commonly not quoted nor is any reference epoch.”
And this: [Only registered and activated users can see links. ]
Extract: “Because Earth is an imperfect ellipsoid, local datums can give a more accurate representation of some specific area of coverage than WGS 84 can. OSGB36, for example, is a better approximation to the geoid covering the British Isles than the global WGS 84 ellipsoid.”
Haven’t you ever wondered why your country that developed GPS still spends enormous resources refining and adjusting your current – official - US local datum NAD83? And why all the other countries do the same with their datums? It’s more accurate.
And it also seems you have missed in the link I posted previously that even in your area NAD83 has a number of different flavours …one for each of the North America plate, Pacific plate and Mariana plate. Why? Because the coordinates are static, fixed to the plates and move with them.
And your new datum that you will be moving to in a few years - and that is better aligned to GNSS - will still also be split into separate datums, one fixed to each plate for the same reason.
Same with most datums, both our GDA94 and GDA2020 are plate fixed, the coordinates are static on the ground and move with us. Read here very carefully: [Only registered and activated users can see links. ]
Extract: “GDA94 is a ‘plate-fixed’ or ‘static’ coordinate datum based on the International Terrestrial Reference Frame 1992 (ITRF92), held at the reference epoch of 1 January 1994.”
And funnily enough the coordinates of the GDA survey marks I use here are still measuring the same within 1cm around 25 years after I first used them…..
And it certainly does matter which coordinate system you chose and they are definitely not all linear and equidistant. One local example here, look at the NZMG which is mathematically twisted around NZ and needs special calculations. It’s now superseded but maps still exist and are used: [Only registered and activated users can see links. ]
Extract: "NZMG is not based on a geometric projection (transverse Mercator is based on a cylinder). Instead it uses a complex-number polynomial expansion. This has the advantage of exhibiting minimal scale distortion over New Zealand; however it is a projection unique to New Zealand and so can be difficult to use or program into computer software or positioning devices (eg, GPS receivers)."
And there are also many other aspects you apparently haven’t considered, for example how earth curvature is treated as it’s also a significant factor in calculating the distance between points.
I think you are also confused with basic “Accuracy” vs “Precision”. Google it or read here: [Only registered and activated users can see links. ]
Accuracy – this topic - is how close you are to a known true point. Precision is how closely your data points group together, regardless of where you are.
So for a Garmin the accuracy relates to how close you are to the known point…which has to be the ground coordinates it gives you and the spot where you are on the ground. There is no other known or true point, it’s not giving you anything else to measure against including satellites. It doesn’t matter if the coordinates are in either datum, or are right or wrong, it’s simply telling you the distance it thinks you may be from that point on the ground where you are. So you would normally expect the accuracy to be the same under the same time and satellite conditions and your test is not really testing anything.
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