How can L/D Max be both Best Glide speed and Max Range speed?
I'm going to answer with the caveat that I don't have as deep of an understanding of this as I would like, and someone smarter than me may be able to correct or expound on my response.
Best Glide is a purely aerodynamic concept. There is no powerplant involved, so you're simply converting potential energy (altitude) into forward motion, at a rate and L/D ratio that is driven by the angle of attack. It's a simpler concept.
When you add a powerplant into the equation, it gets a lot more complicated. The powerplant itself has modes where it's more efficiently converting fuel energy into thrust, and modes where it's less efficiently doing so. Max Range, therefore, depends not only on aerodynamics, but also how efficient the powerplant is. When you add powerplant dynamics into the equation, you might settle on a best range speed that is different than the purely aerodynamic best glide range speed.
Simply put...

Best Glide is where L/Dmax occurs.
Max Range occurs when (FuelBurn / GroundSpeed) is the lowest.

On a related, but slightly different, note: Piston airplanes and Turbo(fans/jets) behave differently when it comes to producing power at different airspeeds. It's why we generally measure turbofan engines in thrust, and piston engines in horsepower. This difference is why Max Range and Maximum Endurance speeds correlate with Best Climb Angle and Best Glide speeds differently, when you compare pistons to jets.
I hope this helps.