I think the inverter term is used without knowing what it is actually meant.

The inverter in electronics means the DC voltage is inverted into AC voltage. From AC to DC it is called convert. So, the opposite of convert is invert.

In case of DC fan, it is just fan that use DC motor. Some ads get people confused with inverter. It is not an inverter fan but just DC fan 

Like you said, it is just AC to DC. However, if it is just direct AC motor with no conversion, it should be more efficient  ; but it is not due to to nature on how AC motor works.

The AC motor is works efficiently at its designed natural speed which I would say should be more efficient than DC motor, but when the AC fan speed is regulated to operate at various other speed, the efficiency drops thus makes it less efficient. Basically, the speed of an AC motor is dependent on the number of poles it has and the line frequency of the power supply, not on it’s voltage. The pole is created by AC current flowing in another set of coil winding. Since pole number is fixed in AC motor, the frequenct change is used to vary speed. That is why normally when ceiling fan is faulty, spoiled capacitor is normally the main suspect. Fan motor cannot turn 

Unlike AC motor, the DC fan is using permanent magnet to create pole. The motor the speed it regulated by controlling how much current flow through motor winding. This is why the control is precise and waste less energy.

There is no inverter involved here. The inverter is different thing. The inverter technology is used to control AC motor through PWM (Pulse Width Modulation). That is another story. This will make AC motor more efficient by being able to regulate power as required.

My fan use fiber blade. No rust.

The humming sound usually because the slip capacitor is degraded already. I think replacing it can solve the problem. Something less than RM10.