Obviously when the filament diameter is smaller than expected then less material comes out of the extruder and when the filament diameter is larger then more material comes out.

This is however not the only driver. There is also the diameter of the hobbed wheel in the extruder that defines how much filament length comes out. The effective diameter of the hobbed wheel depends on the force the filament is pressed against it and the filament material and temperature.

Additionally the volume of the filament might change with its temperature. The hobbed wheel is where the filament should be cold, the nozzle is there where it is hot.

The filament diameter setting in the slicer can be adjusted to get the best result. Slicers as Slic3d have also a extruder multiplier to correct such effects. Alternatively it should be consider to adjust the setting in the printers firmware (as marlin).