In my car, the fuel gauge is a meter which is a hot wire type of unit. The drive current is obtained from a voltage regulator in the dashboard display unit. The supply voltage is passed through the float variable resistance unit (or sender), in the fuel tank. The current from this unit passes through the meter. because the fuel does slosh around in the tank, the current in the meter does vary somewhat. However, because the meter is a thermal meter, then short term variations in the meter current does not show up as a a temperature variation in the meter. The thermal time constant is long, and this is how the meter reading is stabilised. You will note with this type of fuel gauge, that when the ignition switch is turned to ON, it takes a long time for the meter to reach the proper fuel level reading.
Some of the posts above talk about actual fuel useage and this is done through an algorithm which measures the fuel injection open time. Because the fuel system runs at a constant pressure, Open time of the injectors will correlate with actual fuel consumption. The odometer system will then be able to give fuel useage in Litre per km. (apologies to KISS if I have repeated his post)
Hope this helps.