At Hyatt Aviation we charge our aircraft fees based upon the Tach Hour.
Most flight schools nowadays use the common Hobbs meter to measure flight time. The simple explanation is that the Hobbs meter starts as soon as the battery is turned on. In an airplane there are checklist and preparations made with the battery on but the engine off. Essentially, you are billed as soon as you enter the plane until you exit the plane. Flight time (what you log into your logbook) is also measured from the time you turn the battery on until it is off.
*Tach time is measured from the tachometer reading. The tachometer starts counting when the engine is turned on and stops when the engine is turned off (when the engine is running), when the battery is on before and after starting the engine you are not charged the aircraft fee. Tach time is dependent on the engine settings during the flight, i.e. if you "rev the engine" you run the tachometer faster = more cost.
Example of the difference of a 1 hour (by the clock) flight: