The maximum duration speed uses the minimum amount of fuel necessary to keep an aircraft flying steadily at a given altitude, i.e. without gaining or losing height.
The maximum range speed uses increased fuel burn to fly faster and generally higher, allowing the aircraft to travel as fast as possible while trying to keep drag or air resistance at a reasonable level. The higher you go, the less air resistance you encounter, but this costs fuel.
So you have a trade off between time in the air and total distance covered. It seems counter intuitive that a slow flying aircraft that can stay in the air longer doesn't have the same range as one flying faster and burning more fuel, but that is indeed what happens.