The Second Mismatch: Grid Scale Factor
The moment those same two points get expressed in State Plane or UTM, a second distortion joins the first one. It has nothing to do with elevation at all. It comes from flattening a curved surface onto a plane, and it depends entirely on where in the projection zone the two points happen to sit.
A map projection is exactly correct along one line or point, and increasingly stretched or compressed the farther a project sits from it. That distortion, called the grid scale factor, is a second, separate cause of a GNSS-versus-ground mismatch, layered on top of the elevation effect from the last chapter rather than replacing it.
Exactly Right Somewhere, Slightly Off Everywhere Else
Every State Plane zone and every UTM zone is built around a specific line, or in many designs a pair of lines, where scale factor equals exactly one. A Lambert-style zone, common in states that stretch mostly east to west, uses two standard parallels for this, with scale factor running slightly under one between them and slightly over one beyond them. A Transverse Mercator-style zone, common in states that stretch mostly north to south, and UTM zones generally, typically set a slightly reduced scale factor right at the central meridian on purpose, so a matching pair of lines on either side of it can carry the exact value instead, keeping the worst distortion at the zone's outer edges smaller than it would otherwise be. Either way, a project's grid scale factor depends on exactly where it sits relative to those specific lines, not simply on how close it is to the middle of the zone.
Grid scale factor is not a flaw in the projection. It is the projection doing exactly what it was built to do, trading a small, predictable amount of distance accuracy for a flat, usable plane.
A Second Number, Independent of the First
Take the same hundred meter baseline from the last two chapters, and put it at a location where the zone's grid scale factor happens to work out to roughly 0.9999, a realistic value for plenty of real projects depending on exactly where they sit relative to the zone's own lines of exact scale. That factor alone shrinks the projected distance by about a centimeter over that hundred meters, on top of the eight millimeters elevation was already responsible for. Move the same baseline to a different location within the same zone, and the grid scale factor changes accordingly, larger in one direction, smaller in another, while the elevation effect from the last chapter stays exactly the same, since it never depended on position within the zone at all.
Grid scale factor and the elevation effect from the last chapter are not the same distortion described two different ways. One depends entirely on where a project sits inside a projection zone. The other depends entirely on elevation above the ellipsoid. A project can be affected by one, the other, both, or, right at a zone's line of exact scale and at sea level, effectively neither.
Why a GNSS User Runs Into This by Default
A GNSS rover reporting a State Plane or UTM coordinate is already living inside this distortion, whether or not anyone chose to think about it. Grid scale factor is not an optional setting to opt into. It is a property of the projection the instant a projected coordinate is being used at all, exactly the same way that using a flat distance instead of an angle was never really optional either, once a stakeout or a plan dimension needed one.
A project sits very close to a Transverse Mercator zone's central meridian. Does that guarantee grid scale factor is at its smallest there? Not necessarily. Many such zones deliberately set a reduced scale factor at the central meridian itself, so the smallest distortion actually occurs somewhat away from it, along a specific line the zone was designed around, not automatically at the center.
Grid scale factor is a second, independent distortion, caused by a project's position inside a projection zone rather than by elevation. It stacks on top of the elevation effect from the last chapter rather than replacing it, and both are already present the moment a GNSS user is working in a projected coordinate system at all.
Two separate distortions, one from elevation, one from position inside a zone, do not simply sit side by side. They multiply together into a single, practical number worth knowing by name.