https://www.gps.gov/systems/gps/performance/accuracy/
There are many things that contribute to accuracy of GPS, only some of which relate to the device and some of which relate to the user. Even in what I consider the most controlled circumstances that I can provide, there is considerable variability.
Use Case 1 - Stem Mounted, Garmin 520 Cycling GPS and my last 100 bicycle commutes to work, all following the same route. I zoomed in on a corner as that had the largest amount of visible deviation.
Use Case 2 - Pocket Mounted Apple iPhone 6s and my last 100 times walking my dog in the neighborhood. Again I zoomed in on a corner.
There aren't walls or cliffs or other obstructions in these corners. There are leafs and ice and snow and other seasonal changes.
Use Case 3 - Backpack mounted Garmin 76CSx, Out-and-Back in a snowshoe track.
FWIW,
Tim
While I don't feel very qualified to talk about most of everything else discussed in this thread, I know a thing or two about GPS. What you see above, especially the last image, are very typical of consumer-level GPS units (a lot of which use the same SIRFstar chip) - 1Hz update rate, tracks all over the place. Even on multiple outings your tracks will not overlap. Accuracy depends on where you are in the world, how many satellites are overhead, where they are in the sky, what the tree canopy looks like, what the cloud layer looks like, what's going on in the troposphere/ionosphere... so - accuracy of several meters (<7.8 with 95% probability).
If - like already mentioned - you can get a signal from a differential station (DGPS), you can bring that down to 10-15cm.
If you have several thousand $ to burn and you can get an internet signal in the mountains, you can get an RTK (real-time kinematics) correction that brings you down to 1cm. Yes, survey-grade 1 centimeter! And you can pay to get updates more often than 1Hz. Having most of my experience with jumpy consumer-level devices, it was kind of amazing and unbelievable to see how steady and precise RTK-DGPS can be.