What's the direct cause of the burning out of the electrical components? the overvoltage or the current?

Electrical appliances are designed to work at specified voltage,generally based on voltage supplied to homes.The wattage decides the current the device can draw at the specified voltage.If the voltage goes much beyond the specifed limit, current flows through the device far in excess.which in turn generates a lot of heat ,beyond the capacity which the appliance can dissipate safely(.with out catching fire)  Hence burns out.

If the component is in its original physical condition, overvoltage is usually the problem because
the voltage determines the current.

Probably components fail just as often from physical damage of some kind, such as short circuits - where two parts of the device that should be eeparated somehow touch, allowing excessive current to flow because they provide a low-resistance path. Short circuits often result from deterioration of insulation through age or heat.

Sometimes bits of the device burn out, like the filaments in a light bulb or the heating wire in an
electric heater or toaster. This is due to evaporation (in the light bulb) or oxidation as the device
is used.  Usually you will see a flash when the device is turned on. This is because when the filament or heating wire is cold, its resistance is much lower than when it is at operating temperature. A very large current flows and heats the weakest point of the wire to the point where it literally explodes. So again it is voltage that determines the destructive current, though it is not strictly an overvoltage in these cases.

The escape of the smoke, that the manufacturer has incorporated within the structure of the electrical component.
Once the smoke is allowed to escape, it is impossible to get it back in. So, the component must be replaced.