I'm one of the studs that needs to have the diff between DME and ATD clarified.
File this under "things nobody cares about after you finish flight training"...
For the purposes of GPS navigation, fixes don't have an altitude assigned. They simply "float" at whatever altitude the airplane happens to be at at a given point in time. On the other hand, ground based navaids (VORs, NDBs, ILSs etc) have altitudes associated with the transmitter.
DME is the distance from the aircraft's receiver to the navaid's transmitter. So the distance is not only dependent on how far you are from the transmitter but also how high above it you are (a^2+b^2=c^2). Along track distance (ATD) is the straight line distance between you and the GPS coordinates (with no altitude assigned) of the fix you are approaching.
For example, say we are approaching XYZ VOR (which is at sea level). We are 10 miles from the VOR at 10,000 feet. If we load up XYZ in a GPS it will show that we are 10 miles from the VOR. However, if we tune in the DME on the XYZ VOR we will show 10.1 miles.
To verify that we find our height in nautical miles (10,000/6076=1.65) and then square that (2.71) and add it to our ATD from the VOR (10 miles) squared (100). That gives us 102.71. We take the square root of that and we get 10.13.
GPS ATD is considered a suitable substitute for DME because the only time distances like that are critical is close to the ground where the height leg of the Pythagorean triangle is very small and the delta between DME and ATD is negligible. In the flight levels the delta increases, but up there, turning .5 miles early (or late) doesn't matter so much.
Also, I'm digging back about 10 years to remember all of this, so possibly a current instructor can explain it much better.