W_D has it right. I've worked with the data files a GPS records, distance is measured with a series of lat/long points.

You can adjust the distance between recorded points on most GPS units, and the finer grain you select provides a more accurate account of the distance you've traveled.

A GPS can also record an elevation profile. This will show you the ups and downs you traveled, but that is not the same as the distance you traveled.

Distance is measured on a two dimensional plane. If you view an elevation profile on a graph you'll see the miles shown on the graph are not adjusted to elevation.

They are not adjusted on for elevation on your GPS track either, but that's as it should be. If you buy a square mile of land the boundaries would be pretty wonky if they took terrain into account when measuring the mile. There are old jokes about getting more land for your money here in the Ozarks based on that.

Many GPS units have a "Measuring tool" built in. It will show you the distance between your location and the curser on the screen. You can use that to see how the topography is not accounted for when displaying the distance between to points.