Sorry, in level flight where lift equals weight and is constant, and drag is at a minimum, you have found your best lift/drag ratio. So Vmd is, in fact, the speed in level flight that gives the angle of attack for best L/D. We agree that best L/D is the speed to fly for best glide angle. The speed that requires minumum power, which is drag times speed, in level flight is lower than Vmd. Graphically, it is where the speed and drag values form a square that touches the drag curve. This is the speed to fly if you want to use up your potential energy, your height, at the lowest rateand that is minimum sink speed.
Dick W