Ummm - clearly the unit of measure used will determine the actual distance traveled. This is where CHAOS enters into the equation. Its like how many miles long is the west British coast? Now using a mm long measuring device and going around every rock and nuance, how long is it? The answer approaches infinity as the unit of measure shrinks.

A gps adds the horizontal distance between the points where it takes a data sample. If it is set to sample every minute and you meander, the distance covered will be less than if it samples every half minute, etc.

Of course the GPS will say the two waypoints are .87 miles apart. If you really did travel in a straight line up hill at 30 degrees, it would say .87 miles on its odometer - the sum of the horizontal distances between the data points.
Jim