What is the difference between nautical air miles and nautical ground miles?
A nautical ground mile is one nautical mile over the ground.  A nautical air mile is one nautical mile through the air mass.  This distance can be different because of wind.
For example:
If you are flying at 100 knots true airspeed in a zero wind condition, nautical ground miles will equal nautical air miles.
However, if you are flying at 100 knots true airspeed into a 100 knot headwind, your nautical ground miles will alway be zero, regardless of how many nautical air miles you fly for (at 100 knots).
Anything in between will result in some variance affecting the “net displacement of the aircraft”.  This variance can be calculated using the basic wind triangle.