If you go up vertial 1000 feet and didn't travel much horizontally lets say ust 10 feet does DJI record the vertical distances as part of "distance" travelled?  Ie, will it record total distance travelled as 10 feet for this session or is it 1010 feet?

I think it is only the horizontal distance captured by the change in GPS coordinates. Someone else may confirm this.

Or maybe it records the length of the flight path?  In this example we could assume a diagonal line, the hypotenuse of a triangle joining 10ft horizontal with 1000ft vertical, giving 1000.05 feet.

I replayed the first few seconds after takeoff of a recent flight record in the Go app.  I climbed to 2m and moved about 1.5m away from the home point.  It showed the Flight Distance having recorded 2.5m.
Using the formula a² + b² = c² to determine the length of the hypotenuse:

Pythagoras' Theorem: "In a right angled triangle, the area of the square on the hypotenuse equals the sum of the squares on the other two sides."

2² + 1.5² = c²
c² = 6.25
c = √6.25
c = 2.5

Therefore it appears it is measuring the length of the flight track, not the distance or height.  These measurements will be derived from the inbuilt accelerometer, not the GPS as the height in particular is not reliably accurate.

It's horizontal distance.  Vertical distance is ignored.  And yes, I believe it's the total horizontal distance travelled.  Distance from home point is not involved in the calculation.