I had a look at 'Jet Airplane Performance' , chapter 5, by Lufthansa Consulting.
Thatīs what they are saying (at least for jet aircraft):
Max Endurance:
Lines of constant fuel flow (under consideration of altitude and temperature) can be added to the drag-diagram. These lines have a negative slope. The tangency point of each curve group locates the value for minimun fuel. At the same time, these points represent the speed at which the airplane will remain airborne the longest, referred to as 'maximum endurance' . Since these fuel lines have a negative slope max endurance speed is below Vmd. As has been pointed out before for speed stability reasons a higher speed, closer to Vmd, is used when holding.
Max Range:
Similar to fuel flow, specific range lines can be included in the drag-diagram (with consideration to altitude). These lines have a positive slope. The tangency points of both curve groups locate the speed schedule for maximum range under the appropriate conditions.
In summery max endurance is below Vmd amd max range is above Vmd.
Appologies for not being able to include any diagrams. I know a picture says more than 1000 words.